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Automatic Control, IEEE Transactions on

Issue 9 • Date Sept. 1988

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Displaying Results 1 - 21 of 21
  • Comments, with reply, on "Computational algorithms for pole assignment" by N.K. Nichols

    Page(s): 892 - 894
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (267 KB)  

    Some points of the paper by N.K. Nichols (see ibid., vol.AC-31, p.643-5, 1986), concerning the robust pole assignment of linear multiinput systems, are clarified. It is stressed that the minimization of the condition number of the closed-loop eigenvector matrix does not necessarily lead to robustness of the pole assignment. It is shown why the computational method, which Nichols claims is robust, is in fact numerically unstable with respect to the determination of the gain matrix. In replying, Nichols presents arguments to support the choice of the conditioning of the closed-loop poles as a measure of robustness and to show that the methods of J Kautsky, N. K. Nichols and P. VanDooren (1985) are stable in the sense that they produce accurate solutions to well-conditioned problems.<> View full abstract»

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  • Comments on "A simple proof of Kharitonov's theorem" by K.S. Yeung and S.S. Wang

    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (126 KB)  

    It is pointed out that the results of the note by K.S. Yeung and S.S. Wang (see ibid., vol.AC-32, p.822-3, 1987) are already available in the literature.<> View full abstract»

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  • Optimal nonzero set point regulation via fixed-order dynamic compensation

    Page(s): 848 - 852
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (304 KB)  

    Standard LQG (linear quadratic Gaussian) theory is generalized to a regulation problem involving specified nonzero setpoints for the state and control variables and nonzero-mean disturbances. For generality, the results are obtained for the problem of fixed-order (i.e. not necessarily full order) dynamic compensation. When the state control, and disturbance offsets are set to zero and the compensator order is set equal to the plant dimension. The standard LQG result is recovered. These results provide the dynamic counterpart for the nonzero set point regulation results obtained by D.S. Bernstein and W.M. Haddad (1987) by means of static controllers View full abstract»

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  • Design of a stable state feedback controller based on the multirate sampling of the plant output

    Page(s): 812 - 819
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (704 KB)  

    A new type of controller is proposed which detects the ith plant output Ni times during a period of T0 and changes the plant inputs once during T 0. It is shown that an arbitrary state feedback can be realized by such controllers if the plant is observable. This implies, for instance, that arbitrary symmetric pole assignment is possible if the plant is controllable. It is also shown that, if the plant has no zeros at the origin, the state transition matrix of the controller itself can be set arbitrarily without changing the state feedback to be realized. That is to say, inversely expressed, any state feedback can be equivalently realized by a controller with any prescribed degree of stability View full abstract»

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  • On the expectation of the product of four matrix-valued Gaussian random variables

    Page(s): 867 - 870
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    The formula for the expectation of the product of four scalar real Gaussian random variables is generalized to matrix-valued (real or complex) Gaussian random variables. As an application of the extended formula, a simple derivation is presented of the covariance matrix of instrumental variable estimates of parameters in multivariable regression models View full abstract»

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  • Stabilizability of linear time-varying and uncertain linear systems

    Page(s): 884 - 887
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (344 KB)  

    Feedback stabilization of linear time-varying and uncertain linear systems is considered. It is proved that given a stabilizing dynamic linear state-feedback controller, one can always construct a stabilizing nondynamic linear state-feedback controller. A similar result is shown for uncertain linear systems. A linear time-varying system can be stabilized by dynamic output feedback if and only if it admits a coprime factorization View full abstract»

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  • A study of controllability and time-optimal control of a robot model with drive train compliances and actuator dynamics

    Page(s): 852 - 856
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (384 KB)  

    The problems of robot controllability and time-optimal control where drive train compliances and actuator dynamics are incorporated in the mathematical model are considered. Conditions that ensure the existence of a time-optimal control, are demonstrated, and controllability of the augmented model (robot and actuator) in open-and-closed-loop form is established. A procedure is described for the derivation of easily computable functional inequalities which represent upper bounds on the norm of the augmented system's time response View full abstract»

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  • Stability theory for linear time-invariant plants with periodic digital controllers

    Page(s): 820 - 832
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (824 KB)  

    The control of a linear time-invariant plant by a digital controller composed of a sampler, a periodic discrete-time component, and a zero-order hold is considered. The stability of such a configuration is analyzed. It is shown how closed-loop zeros can be placed using such a scheme. As a consequence, it is proved that the gain margin can be arbitrarily assigned by suitable choice of sampling time and digital controller. The design procedure is constructive, using state-space methods View full abstract»

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  • Robust state feedback stabilization of discrete-time uncertain dynamical systems

    Page(s): 887 - 891
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (344 KB)  

    The problem of stabilization of a class of discrete-time dynamic systems containing uncertain elements, using the direct method of Lyapunov, is considered. State feedback controllers that guarantee uniform boundedness and uniform ultimate boundedness of the closed-loop system are proposed View full abstract»

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  • Generalized Bezoutians and invariant subspaces

    Page(s): 880 - 883
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (468 KB)  

    Given a controllable and observable linear time-invariant system for which the transfer matrix has a right and left coprime matrix fraction description, the generalized Bezoutian of the matrix polynomials of the matrix fraction description is shown to be related to the right (A,B)-invariant vectors and the left (C,A)-invariant vectors View full abstract»

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  • Some results on robust stability of discrete-time systems

    Page(s): 844 - 847
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (336 KB)  

    The theorem of Kharitonov on the Hurwitz property of interval families of polynomials cannot be extended, in genera, to obtain sufficient conditions for the stability of families of characteristic polynomials of discrete-time systems. Necessary and sufficient conditions for this stability problem are given. Such conditions naturally give rise to a computationally efficient stability test which requires the solution of a one-parameter optimization problem and which can be considered as a counterpart to the Kharitonov test for continuous-time systems. At the same time, the method used to derive the stability conditions provides a procedure for solving another stability robustness problem, i.e. the estimation of the largest domain of stability with a rectangular box shape around given nominal values of the polynomial coefficients View full abstract»

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  • On the construction of certain Dulac functions

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    Using methods for the construction of Lyapunov functions, some Dulac functions are obtained that assure the nonexistence of closed paths for second-order dynamical systems View full abstract»

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  • Robust estimation and filtering in the presence of bounded noise

    Page(s): 864 - 867
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (328 KB)  

    Optimal algorithms for robust estimation and filtering are constructed. The noise is considered a deterministic variable belonging to a set described by a norm. Previous results, obtained for complete (one-to-one) and approximate information by M. Milanese and R. Tempo (ibid., vol.30, p.730-8, 1985), are extended to partial and approximate information. This information is considered useful in dealing with dynamic systems not completely identifiable and/or with two different sources of noise, such as process and measurement noise. For different norms characterizing the noise, optimal algorithms (in a min-max sense) are shown. In particular, for Hilbert norms a linear optimal algorithm is the well-known minimum variance estimator. For l norm an optimal algorithm, computable by linear programming, is presented. State estimation is formalized in the context of the general theory. For stable systems, an approximate state estimation is obtained by neglecting higher order powers. An upper bound determining the approximation introduced is derived. A numerical example illustrates the application of the theory View full abstract»

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  • A state-space approach to super-optimal H control problems

    Page(s): 833 - 843
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (636 KB)  

    A numerically stable algorithm is presented for solving the strengthened (or super-optimal) model-matching problem. The steps of the algorithm follows closely those given by N.J. Young (1986) except that for each step a reliable implementation using state-space models is provided View full abstract»

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  • A full invariant under dynamic output feedback: a generalized inverse approach

    Page(s): 883 - 884
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    A novel full invariant of linear time-invariant multivariable systems under causal dynamic output feedback is derived. It makes use of a generalized inverse approach View full abstract»

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  • The VSS approach to the model reference control of nonminimum phase linear plants

    Page(s): 859 - 863
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (388 KB)  

    A nontrivial application of the discontinuous control system theory, based on Filippov's solution concept, is presented. The problem addressed is the model reference output feedback control of linear plants with non-Hurwitzian numerator in the transfer function. A solution in the case of known systems is presented first. An error state equation, whose state is accessible, is then derived for the case in which the plant parameters are unknown. In the case in which some bounds on the plant characteristics are supposed known, a pair of discontinuous signals acting on both the plant and the model is chosen, causing the error state to vanish asymptotically View full abstract»

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  • Two properties of l1-optimal controllers

    Page(s): 876 - 878
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    The solution of the l1 sensitivity minimization problem is shown to have two properties which contrast markedly with properties of the solutions to the better-known H∞ sensitivity minimization problem or the LQG (linear quadratic Gaussian) problem is given of a one-parameter family of first-order plants where the order of the l1-optimal compensator can be arbitrarily large, and thus it is impossible to bound the order of an l1-optimal compensator in terms of the order of the plant. A plant is considered which has a continuous one-parameter family of l1-optimal compensators, and thus l1-optimal compensators need not be unique. The author's two examples are considered to answer two questions left open by M.A. Daleh and J.B. Pearson (ibid., vol.32, p.314-23, 1987) View full abstract»

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  • A model reference adaptive control scheme for pure-feedback nonlinear systems

    Page(s): 803 - 811
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (624 KB)  

    A model reference adaptive control (MRAC) scheme is presented for nonlinear systems in a pure-feedback canonical form with unknown parameters. The present of parameter uncertainty in the system causes imperfect linearization, i.e. it introduces nonlinear additive terms in the transformed coordinates. Under some mild technical assumptions, global convergence of the output error is established for all initial estimates of the parameter vector lying in an open neighborhood of the true parameters in the parameter space View full abstract»

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  • Feedback linearization of sampled-data systems

    Page(s): 857 - 859
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    It is shown that feedback linearizability of a continuous-time system can be destroyed through the introduction of the usual sample-and-hold devices. A method whereby a feedback linearizable discrete-time model can be recovered is given View full abstract»

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  • An algorithm for pole assignment in high order multivariable systems

    Page(s): 870 - 876
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (600 KB)  

    An efficient computational method is presented for solving the problem of pole assignment by state feedback in linear multivariable systems with large dimensions. A given multiinput system is first transformed to an upper block Hessenberg form by means of orthogonal state coordinate transformations. The state feedback problem is then reformulated in terms of the Sylvester equation. The transformed system matrices, along with certain assumed block forms for unknown matrices, enable the Sylvester equation to be decomposed and solved effectively. A distinct point of the proposed algorithm is that the solution procedure can be tailored to parallel implementation and is therefore fast. Computational aspects of the algorithm are discussed and numerical examples are provided View full abstract»

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  • A note on reduced-order controller synthesis

    Page(s): 878 - 880
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (240 KB)  

    It is proposed that reduced-order controllers for single-input single-output plants may be synthesized by first calculating a controller for some, not necessarily accurate, reduced-order model of the plant, and then refining the controller so as to account for the full plant. The controller refinement is formulated in terms of a model-approximation problem within a feedback loop. Closed-loop stability is then guaranteed provided that the approximation error is below a certain bound 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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Editor-in-Chief
P. J. Antsaklis
Dept. Electrical Engineering
University of Notre Dame