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Automatic Control, IEEE Transactions on

Issue 12 • Date Dec. 1994

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Displaying Results 1 - 25 of 25
  • Comments on "Stability margin evaluation for uncertain linear systems

    Publication Year: 1994 , Page(s): 2523 - 2524
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (159 KB)  

    The bound derived in the above paper by Gong-Thompson (ibid. vol.39, no.3, p.548-50 (1994)) is shown via two new stability criteria not to be the tightest possible for all unstructured perturbations. A minor error of their theorem is also corrected.<> View full abstract»

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  • Comments on "Vector norms as Lyapunov functions for linear systems" [with reply]

    Publication Year: 1994 , Page(s): 2522 - 2523
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (91 KB)  

    The purpose of this note is to give a counterexample to a possible implication of the main result of the above paper by Kiendl-Adamy-Stelzner (ibid., vol.37, no.6, p.839-42 (1992)), to modify this result, to restate its theorem accordingly, and to supply a proof for it. In reply, Kiendl et al. point out that they did not formulate the condition as necessary for a vector norm being a Lyapunov function. Due to Hmamed's remarks, they have reviewed their statements for imprecise formulations.<> View full abstract»

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  • A property of the Routh table and its use

    Publication Year: 1994 , Page(s): 2494 - 2496
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (236 KB)  

    Starting from a given polynomial, the Routh algorithm recursively generates a family of all-pole transfer functions with the same energy of the impulse response and a suitable number of its derivatives. It is shown that each of these energies is given by a linear combination of some of the others according to the entries of a row of the Routh table for the given polynomial. This fact can be exploited to evaluate certain quadratic integrals in an efficient way View full abstract»

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  • Properties of the entire set of Hurwitz polynomials and stability analysis of polynomial families

    Publication Year: 1994 , Page(s): 2490 - 2494
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (424 KB)  

    It is proved in this paper that all Hurwitz polynomials of order not less than n form two simply connected Borel cones in the polynomial parameter space. Based on this result, edge theorems for Hurwitz stability of general polyhedrons of polynomials and boundary theorems for Hurwitz stability of compact sets of polynomials are obtained. Both cases of families of polynomials with dependent and independent coefficients are considered. Different from the previous ones, our edge theorems and boundary theorems are applicable to both monic and nonmonic polynomial families and do not require the convexity or the connectivity of the set of polynomials. Moreover, our boundary theorem for families of polynomials with dependent coefficients does not require the coefficient dependency relation to be affine View full abstract»

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  • Controllability of spacecraft systems in a central gravitational field

    Publication Year: 1994 , Page(s): 2426 - 2441
    Cited by:  Papers (16)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1256 KB)  

    The configuration space for rigid spacecraft systems in a central gravitational field can be modeled by SO(3)× IR3, where the special orthogonal group SO(3) represents the attitude dynamics and IR3 is for the orbital motion. The attitude dynamics of the spacecraft system is affected by the orbital elements through the well-known gravity-gradient torque. On the other hand, the effects of attitude-orbit coupling can also possibly be used to alter orbital motions by controlling the attitude. This controllability property is the primary issue of this paper. The control systems for spacecraft with either reaction wheels or gas jets being used as attitude controllers are proven in this study to be controllable. Rigorously establishing these results necessitates starting with the formal definitions of controllability and Poisson stability. It is then shown that if the drift vector field of the system is weakly positively Poisson stable and the Lie algebra rank condition is satisfied, controllability can be concluded. The Hamiltonian structure of the spacecraft model provides a natural route of verifying the property of weakly positive Poisson stability. Accordingly, the controllability is obtained after confirming the Lie algebra rank condition. Developing a methodology in deriving Lie brackets in the tangent space of T(SO(3)×IR3), i.e., the second tangent bundle is thus deemed necessary. A general formula is offered for the computation of Lie brackets of second tangent vector fields in TT(SO(3)m×IRn), in light of its importance in the fields of mechanics, robotics, optimal control, and nonlinear control, among others. With these tools, the controllability results can be proved. The analysis in this paper gives some insight into the attitude-orbit coupling effects and may potentially lead towards new techniques in designing controllers for large spacecraft systems View full abstract»

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  • Inequalities for the trace of matrix product

    Publication Year: 1994 , Page(s): 2489 - 2490
    Cited by:  Papers (16)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (160 KB)  

    To obtain estimates of solutions of Lyapunov and Riccati equations which frequently occur in the stability analysis and optimal control design in linear control theory, many researchers have attempted to determine upper and lower bounds for the product of two matrices in terms of the trace of one matrix and the eigenvalues of the other. Baksalary and Puntanen claimed (“An inequality for the trace of matrix product”, ibid., vol. 37, no. 2, p. 239-40, 1992) that they had obtained a better estimate for the trace of the product of two matrices. The purpose of this note is to point out that their main result is incorrect and a counterexample is presented View full abstract»

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  • Routh-Pade approximation for interval systems

    Publication Year: 1994 , Page(s): 2454 - 2456
    Cited by:  Papers (17)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (216 KB)  

    Presents a method for the reduction of the order of interval system. The denominator of the reduced model is obtained by a direct truncation of the Routh table of the interval system. The numerator is obtained by matching the coefficients of power series expansions of the interval system and its reduced model. A numerical example illustrates the proposed procedure View full abstract»

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  • A unified theory of full-order and low-order observers based on singular system theory

    Publication Year: 1994 , Page(s): 2497 - 2502
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (528 KB)  

    The standard construction of the minimal-order state observer for a linear time-invariant plant is shown to be a degenerate form of the ordinary full-order observer. The naive state estimation technique of successively differentiating the plant output is also shown to be a limiting case of the same full-order structure. Various results concerning the set of all degenerate forms of the full-order observer are presented. In particular, conditions are established under which shifting observer eigenvalues far to the left in the complex plane implies proximity to a successively differentiating system. In addition, it is shown that such a scheme can never yield satisfactory estimation. Singular perturbation and singular system theory are used throughout the analysis View full abstract»

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  • 2-optimal design of multirate sampled-data systems

    Publication Year: 1994 , Page(s): 2506 - 2511
    Cited by:  Papers (21)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (464 KB)  

    Treating causality constraints, this paper studies optimal synthesis of multirate sampled-data systems with an ℋ2 performance criteria. An explicit solution is obtained by input-output space extensions (lifting) and frequency-domain techniques View full abstract»

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  • An exact solution to general SISO mixed H2/H problems via convex optimization

    Publication Year: 1994 , Page(s): 2511 - 2517
    Cited by:  Papers (9)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (576 KB)  

    The mixed H2/H control problem can be motivated as a nominal LQG optimal control problem, subject to robust stability constraints, expressed in the form of an H norm bound. A related modified problem consisting on minimizing an upper bound of the H2 cost subject to H constraints was introduced by Bernstein-Haddad (1989). Although there presently exist efficient methods to solve this modified problem, the original problem remains, to a large extent, still open. In this paper we propose a method for solving general discrete-time SISO H2/H problems. This method involves solving a sequence of problems, each one consisting of a finite-dimensional convex optimization and an unconstrained Nehari approximation problem. View full abstract»

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  • A common Lyapunov function for stable LTI systems with commuting A-matrices

    Publication Year: 1994 , Page(s): 2469 - 2471
    Cited by:  Papers (166)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (288 KB)  

    The paper demonstrates that a common quadratic Lyapunov function exists for all linear systems of the form x˙=Aix, i=1,2,···,N, where the matrices Ai are asymptotically stable and commute pairwise. This in turn assures the exponential stability of a switching system x˙(t)=A(t)x(t) where A(t) switches between the above constant matrices Ai View full abstract»

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  • An analytical method of estimating the domain of attraction for polynomial differential equations

    Publication Year: 1994 , Page(s): 2471 - 2475
    Cited by:  Papers (12)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (372 KB)  

    A system of nth-order differential equations with polynomial right-hand sides is considered, and a simple analytical method of estimating the domain of attraction is developed. The method involves an ordinary quadratic Lyapunov function υ=XTQ(Y)X with a certain parameter vector Y from the same state space. All linear factors in the expression for υ˙ are bounded in the domain υ⩽1, and the derivative is bounded by a quadratic function, the negativeness of which determines the restrictions for Y. The domain of attraction is estimated through a simple scaling of the obtained area or through its nonlinear transformation with optimization. The method allows for obtaining domains (for example, with infinite volume) that are comparable with ones obtained by complicated computational procedures. A set of examples is presented View full abstract»

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  • A general result on the stabilization of linear systems using bounded controls

    Publication Year: 1994 , Page(s): 2411 - 2425
    Cited by:  Papers (198)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1164 KB)  

    We present two constructions of controllers that globally stabilize linear systems subject to control saturation. We allow essentially arbitrary saturation functions. The only conditions imposed on the system are the obvious necessary ones, namely that no eigenvalues of the uncontrolled system have positive real part and that the standard stabilizability rank condition hold. One of the constructions is in terms of a “neural-network type” one-hidden layer architecture, while the other one is in terms of cascades of linear maps and saturations View full abstract»

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  • Control problems in super-articulated mechanical systems

    Publication Year: 1994 , Page(s): 2442 - 2453
    Cited by:  Papers (26)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (996 KB)  

    Control of super-articulated mechanical systems (SAMS: controlled mechanical system in which the dimension of the configuration space exceeds the dimension of the control input space) is studied. As a starting point, a graphical characterization of general SAMS is developed in which a so-called control flow diagram (CFD) is constructed to represent the interaction forces among the degrees of freedom of the system; three types of structure, namely, the chain structure, the tree structure and isolated points, are identified; degree of complexity of the system is defined based on the structure of the system. A systematic backstepping type controller design is proposed for systems with a chain structure to achieve global asymptotic stability and trajectory tracking. Such a controller design itself illustrates the sufficient conditions for the existence of smooth feedback control such that the systems with a chain structure can be globally asymptotically stabilized. The connection of the authors' control algorithm with existing results is discussed View full abstract»

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  • Robust stability of time-delay systems

    Publication Year: 1994 , Page(s): 2388 - 2397
    Cited by:  Papers (35)  |  Patents (6)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (800 KB)  

    There are two fundamental results available when we study stability of a polynomial family that is described by convex polytope in the coefficient space: the edge theorem and the theory based on the concept of convex directions. Many known results can be explained with these two results. This paper deals with a generalization of this line of research to the case of quasipolynomials that are entire functions which include both degree of the independent variable and exponential functions. The main objects of the paper are the developing of the concept of convex directions for quasipolynomials and exploiting this concept for construction of testing sets for quasipolynomial families. One of the primary sources of motivation for the class of problems considered in this paper is derived from process control. A typical problem formulation almost always includes a delay element in each subsystem process block. When we interconnect a number of such blocks in a feedback system, the study of robust stability involves quasipolynomials of the sort considered in this paper View full abstract»

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  • The row by row decoupling problem with stability: a structural approach

    Publication Year: 1994 , Page(s): 2457 - 2460
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (352 KB)  

    The row by row decoupling problem with stability via regular static state feedback is revisited here for linear systems. A new geometric characterization is provided which easily lends to a nice structural solution expressed in terms of infinite and unstable contents View full abstract»

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  • On the generalized q-Markov cover models for discrete-time systems

    Publication Year: 1994 , Page(s): 2502 - 2505
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (332 KB)  

    A new method for obtaining generalized q-Markov cover models for discrete-time SISO systems is proposed and is based on the inverse solution of the Lyapunov equation. The reduced order models not only match the Markov parameters and high-frequency power moments like the conventional q-Markov cover techniques but also match time moments and low-frequency power moments of the original system View full abstract»

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  • Optimal filtering in stochastic discrete-time systems with unknown inputs

    Publication Year: 1994 , Page(s): 2461 - 2464
    Cited by:  Papers (6)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (368 KB)  

    In this note we derive a recursive filtering algorithm for the linear discrete-time dynamic system with indeterminate-stochastic inputs. The algorithm is based on the minimax-optimal method of parameter estimation in the linear regression model with parameters of two different types: unknown and stochastic with partially known characteristics View full abstract»

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  • control of nonlinear systems via output feedback: controller parameterization

    Publication Year: 1994 , Page(s): 2517 - 2521
    Cited by:  Papers (9)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (384 KB)  

    The standard state space solutions to the ℋ control problem for linear time-invariant systems are generalized to nonlinear time-invariant systems. A class of local nonlinear (output feedback) ℋ-controllers are parameterized as nonlinear fractional transformations on contractive, stable nonlinear parameters. As in the linear case, the ℋ control problem is solved by its reduction to state feedback and output estimation problems, together with a separation argument. Sufficient conditions for ℋ-control problem to be locally solved are also derived with this machinery View full abstract»

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  • On stability and performance of sampled-data systems subject to wordlength constraint

    Publication Year: 1994 , Page(s): 2476 - 2481
    Cited by:  Papers (31)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (468 KB)  

    In this paper we study the effects of finite-precision controller implementation on the stability and performance of sampled-data systems. A framework is presented in which these effects can be analyzed from a statistical point of view. We analyze the behavior of finite-precision controllers at fast sampling rates and consider the problem of L 2-induced norm minimization, subject to a wordlength constraint View full abstract»

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  • On absolute stability of differential-delay systems

    Publication Year: 1994 , Page(s): 2481 - 2484
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (276 KB)  

    A nonlinear differential-delay system with many nonlinearities is studied. A new absolute stability criterion is derived View full abstract»

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  • A robust MIMO terminal sliding mode control scheme for rigid robotic manipulators

    Publication Year: 1994 , Page(s): 2464 - 2469
    Cited by:  Papers (107)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (420 KB)  

    In this paper, a robust multi-input/multi-output (MIMO) terminal sliding mode control technique is developed for n-link rigid robotic manipulators. It is shown that an MIMO terminal switching plane variable vector is first defined, and the relationship between the terminal switching plane variable vector and system error dynamics is established. By using the MIMO terminal sliding mode technique and a few structural properties of rigid robotic manipulators, a robust controller can then be designed so that the output tracking error can converge to zero in a finite time, and strong robustness with respect to large uncertain dynamics can be guaranteed. It is also shown that the high gain of the terminal sliding mode controllers can be significantly reduced with respect to the one of the linear sliding mode controller where the sampling interval is nonzero View full abstract»

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  • Stabilizing control for a class of uncertain interconnected systems

    Publication Year: 1994 , Page(s): 2484 - 2488
    Cited by:  Papers (8)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (400 KB)  

    A linear decentralized control is constructed to stabilize a class of interconnected nonlinear uncertain systems with time-varying state-delay and in which the output measurement is noisy. The control action is based on output-feedback for matched uncertainties and takes the effect of coupling into account. With the knowledge of the uncertainty bounds, it is established that the developed stabilizing controller renders the closed-loop interconnected system “globally practically stable” View full abstract»

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  • Performance analysis and improvement in model reference adaptive control

    Publication Year: 1994 , Page(s): 2370 - 2387
    Cited by:  Papers (38)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1280 KB)  

    The purpose of this paper is to address the issue of performance by using two additional criteria to assess performance in the ideal and nonideal situations. They are the mean square tracking error criterion and the L tracking error bound criterion. We use these criteria to examine the performance of a standard model reference adaptive controller and motivate the design of a modified scheme that can have an arbitrarily improved nominal performance in the ideal case and in the presence of bounded input disturbances. It is shown that for these cases the modified scheme can provide an arbitrarily improved zero-state transient performance and an arbitrary reduction in the size of possible bursts that may occur at steady state. As in every robust control design, the nominal performance has to be traded off with robust stability and therefore the improvement in performance achieved by the proposed scheme is limited by the size of the unmodeled dynamics, as established in the paper View full abstract»

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  • Variable lookahead supervisory control with state information

    Publication Year: 1994 , Page(s): 2398 - 2410
    Cited by:  Papers (10)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1152 KB)  

    In cases where the discrete-event system model has an infinite or large state space, or when it is not completely specified a priori, applying the traditional off-line methods for computing the control policy may be impractical, if not infeasible. We adopt an online limited lookahead approach. Under this approach, the next control action is determined based on an N-step ahead projection of the system behavior and on one of two attitudes-conservative or optimistic. We extend this approach to incorporate knowledge of the system state in the computation. This has the potential of improving the efficiency of the computation as well as the quality of the control policy. There are five specific contributions presented in this paper: 1) a new algorithm for the online computation of supervisory controls with worst case complexity that is quadratic in the number of “expanded” states, 2) an algorithmic proof of the correctness of this algorithm that avoids using fixed point methods and offers new insight into the structure of the supremal controllable sublanguage, 3) an off-line version based on a forward search technique that has the same worst case complexity as existing off-line algorithms but is potentially more efficient, 4) a formal proof of the fact that when the languages of interest are livelock free the computations are performed in linear complexity, and 5) new bounds on the depth of the lookahead window that guarantee optimality View full abstract»

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In the IEEE Transactions on Automatic Control, the IEEE Control Systems Society publishes high-quality papers on the theory, design, and applications of control engineering.  Two types of contributions are regularly considered

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Meet Our Editors

Editor-in-Chief
P. J. Antsaklis
Dept. Electrical Engineering
University of Notre Dame