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Automatic Control, IEEE Transactions on

Issue 9 • Date Sept. 1993

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Displaying Results 1 - 21 of 21
  • Robust stability of linear systems described by higher-order dynamic equations

    Page(s): 1430 - 1435
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    The stability radius of higher-order differential and difference systems with respect to various classes of complex affine perturbations of the coefficient matrices is studied. Different perturbation norms are considered. The aim is to derive robustness criteria that are expressed directly in terms of the original data. Previous results on robust stability of Hurwitz and Schur polynomials are extended to monic matrix polynomials. For disturbances acting via a uniform input matrix, computable formulas are obtained, whereas for perturbations with multiple input matrices, structured singular values are involved.<> View full abstract»

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  • On the duality between routing and scheduling systems with finite buffer space

    Page(s): 1440 - 1446
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    A duality between scheduling and routing problems associated with a set of parallel queues is established. This allows one to determine the optimal policy for either system, once it is determined for its dual system. Moreover, the evaluation of different design alternatives (e.g., allocation of buffers) can be accommodated in the same duality framework. A crucial assumption is that both systems should be Markovian. Furthermore, when there is no buffer at the controller, the scheduling policy is assumed to be preemptive. On the other hand, when there exists buffer space dedicated to the controller, both the routing and scheduling policies are assumed to be nonidling. Various applications are presented. It is shown, for instance, that the smallest residual capacity scheduling policy is optimal, as it is the dual of the well-known shortest queue routing policy View full abstract»

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  • Parameterizations of stabilizing compensators by using reduced-order observers

    Page(s): 1435 - 1439
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    Reduced-order stabilizing compensators are parameterized in terms of doubly coprime factorizations having state-space representations based on a minimal-order observer and its dual observer. A free parameter of the compensators is restricted within strictly proper stable rational functions. The order of the compensators is lower than that of Nett's by the number of outputs or inputs View full abstract»

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  • New sufficient conditions for the stability of slowly varying linear systems

    Page(s): 1409 - 1411
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    The frozen-time approach is used to state some new sufficient conditions for the stability of linear time-varying systems. An upper bound on the norm of the time derivative of system matrix which, under different assumptions on frozen-time system eigenvalues, guarantees asymptotic stability or exponential stability of the system is established View full abstract»

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  • Frequency domain uncertainty and the graph topology

    Page(s): 1371 - 1383
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    A new metric on linear, time-invariant systems is defined. This metric is no greater than the gap metric, and is in fact the smallest metric for which a certain robust stabilization result holds. Unlike other known metrics which induce the graph topology, it has a clear frequency response interpretation. This allows questions regarding robustness in the face of parametric uncertainty to be considered in terms of this metric View full abstract»

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  • Continuous observability for parabolic system under observations of discrete type

    Page(s): 1388 - 1391
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    For the linear partial differential equation of parabolic type, the problem of continuous observability under observations of discrete type received from the moving or stationary sensors is considered. The techniques exploit the knowledge about observability of an associated system with observations that are continuous in time. On the basis of sensitivity points of the latter, a method of constructing discrete observations that preserve the property of continuous observability at final time is developed View full abstract»

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  • Zeros of modal models of flexible structures

    Page(s): 1384 - 1388
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    It is shown that in some situations the zero patterns of a flexible structure change radically with model order. The refinement of the model by the addition of higher-order modes can cause zeros to appear at low frequencies or in the right half-plane. Structures instrumented with piezoelectric actuators and/or fiber-optic sensors are also considered View full abstract»

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  • Stabilization of nonlinear discrete-time systems using state detection

    Page(s): 1398 - 1400
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    Some recent results concerning stabilization of continuous-time systems using state detection are extended to the case of discrete-time nonlinear systems. It is shown that if a discrete-time locally detectable system can be stabilized by a state feedback law, then it can also be stabilized by a feedback law that depends on the output of a weak detector View full abstract»

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  • Acceptable input sequences for singular 2-D linear systems

    Page(s): 1391 - 1394
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    Necessary and sufficient conditions for the acceptance of all input sequences on the given rectangle for singular 2-D linear systems are established. A procedure based on elementary row operations for finding the set of acceptable input sequences is given and illustrated by numerical example View full abstract»

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  • Deflation in eigenvalue assignment of descriptor systems using state feedback

    Page(s): 1322 - 1336
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    It is shown how deflation by unitary equivalence transformations can be used to solve the eigenvalue assignment problem for descriptor systems using state feedback. The system is first transformed to a form that reveals its controllability. The uncontrollable part of the system, if any, is then discarded, and the assignments are continued with the completely controllable part of the system. To give insight into the approach, a mathematical method for the solution is derived, without considering numerical issues, using the idea of deflation. It is shown how this method can be modified to derive a numerically efficient algorithm. The numerical stability of the algorithm is proved and a numerical example is presented View full abstract»

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  • A necessary and sufficient condition for robust asymptotic stability of time-variant discrete systems

    Page(s): 1427 - 1430
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    A necessary and sufficient condition for the stability of time-variant interval matrices is presented. This condition allows stability to be tested by checking only products of vertex (extreme) matrices. The implementation of the test in the form of an algorithm and two illustrative examples are provided View full abstract»

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  • On a weaker notion of controllability of a language K with respect to a language L

    Page(s): 1446 - 1447
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    A necessary and sufficient condition for a prefix-closed language K⊆Σ* to be controllable with respect to another prefix-closed language L⊆Σ* is that KL. A weaker notion of controllability where it is not required that KL is considered here. If L is the prefix-closed language generated by a plant automaton G, then essentially there exists a supervisor Θ that is complete with respect to G such that L(Θ|G)=KL if and only if K is weakly controllable with respect to L. For an arbitrary modeling formalism it is shown that the inclusion problem is reducible to the problem of deciding the weaker notion of controllability. Therefore, removing the requirement that KL from the original definition of controllability does not help the situation from a decidability viewpoint. This observation is then used to identify modeling formalisms that are not viable for supervisory control of the untimed behaviors of discrete-event dynamic systems View full abstract»

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  • On the robust Popov criterion for interval Lur'e system

    Page(s): 1400 - 1405
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    The classical Popov criterion is generalized to include problems with parametric uncertainty, as well as nonlinear sector bounded perturbations. The parametric dependence is modeled by an interval plant description. A robust Popov criterion is obtained for a plant-controller configuration. Stronger external results are obtained for a special class of controllers. An example illustrating the numerical implementation of these results is presented View full abstract»

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  • FIR system identification using fourth-order cumulants with application to channel equalization

    Page(s): 1394 - 1398
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    Three algorithms for finite impulse response (FIR) system identification from output measurements, using fourth-order cumulants, are described. The impulse response is assumed to be complex, and the input is a complex independent and identically distributed (i.i.d) non-Gaussian sequence. The algorithms are based on a certain low-rank matrix constructed from the output cumulants. An application of the algorithms to blind equalization of digital communication channels is discussed and illustrated by some examples View full abstract»

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  • A chain scattering-matrix description approach to H control

    Page(s): 1416 - 1421
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    Chain scattering-matrix descriptions and J-lossless coprime factorizations are employed to develop a relatively simple method for the synthesis of the continuous-time H suboptimal control. Analogously to the Youla parameterization of all stabilizing controllers, the authors derive an identity to generate all suboptimal controllers. The derivation is carried out in terms of transfer function matrices although the final formulas are in state space. The approach provides a clear connection at the transfer function level between coprime factorizations and algebraic Riccati equations that are associated with the solutions of the problem View full abstract»

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  • A novel proof of the Souriau-Frame-Faddeev algorithm

    Page(s): 1447 - 1448
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    A simple and elegant proof is given for a recurrence relation that computes the coefficients of the characteristic polynomial of a linear system used in the Souriau-Frame-Faddeev algorithm View full abstract»

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  • A unifying design of sliding mode and classical controllers

    Page(s): 1422 - 1427
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    A theory is given to unify output sliding-mode control and classical control. The idea is based on defining the sliding variable in such a way that once the system begins to slide, the classical controller transfer function is realized. This idea leads to the development of a hybrid sliding-and-classical controller which retains the merits of both types of controllers but eliminates their respective limitations. The proposed method is robust and applies to non-minimum-phase single-input, single-output (SISO) systems. No state measurement is required View full abstract»

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  • Worst-case analysis and design of sampled-data control systems

    Page(s): 1337 - 1358
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    Sampled-data systems with continuous-time inputs and outputs, where some state variables evolve in continuous time and others evolve in discrete time, are considered. Methods are presented for computing and optimizing the L2-induced norm of such systems, considered as operators relating square integral signals. These worst-case analysis and design results are counterparts of the H-norm analysis and synthesis for purely continuous- or discrete-time systems. The analysis shows that the L 2-induced norm of a sampled-data system is smaller than γ if certain discrete-time descriptor systems have no eigenvalue of magnitude one, and if a certain discrete-time linear time-invariant plant depending on γ has H norm smaller than γ. The synthesis shows that the optimal attenuation problem for a four-block continuous-time plant with a digital controller can be solved with a γ-iteration on a certain discrete-time four-block plant which depends on γ View full abstract»

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  • Semiglobal stabilization of a class of nonlinear systems using output feedback

    Page(s): 1412 - 1415
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    The stabilization of a class of multivariable nonlinear systems, about an equilibrium point at the origin, using output feedback, is considered. In particular, a class of systems which can be transformed into a global normal form with no zero dynamics is treated. Semiglobal stabilization means that for every compact set of initial conditions, an output feedback controller that stabilizes the origin and includes the given compact set in the region of attraction can be designed. The system equations are allowed to depend on constant unknown parameters which do not change the vector relative degree of the system, and the controller is robust with respect to these parameters. Global Lipschitz conditions are not required View full abstract»

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  • The robust H2 control problem: a worst-case design

    Page(s): 1358 - 1371
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    The worst-case effect of a disturbance system on the H 2 norm of the system is analyzed. An explicit expression is given for the worst-case H2 norm when the disturbance system is allowed to vary over all nonlinear, time-varying and possibly noncausal systems with bounded L2-induced operator norm. An upper bound for this measure, which is equal to the worst-case H2 norm if the exogeneous input is scalar, is defined. Some further analysis of this upper bound is done, and a method to design controllers which minimize this upper bound over all robustly stabilizing controllers is given. The latter is done by relating this upper bound to a parameterized version of the auxiliary cost function studied in the literature View full abstract»

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  • An adaptive deadzone technique with a burst alleviation example

    Page(s): 1405 - 1409
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (416 KB)  

    Elements of recursive-least-squares estimation and gradient-least-squares estimation are combined to produce an estimator with an adaptive deadzone. The estimate adjustment shuts off when the error residual is within the deadzone, and the deadzone adapts to the apparent magnitude of the nonparametric uncertainty. Simulation results show successful prevention of bursting without prior knowledge of the nonparametric uncertainty View full abstract»

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Aims & Scope

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