Stabilization Problem

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Patrizio Colaneri - One of the best experts on this subject based on the ideXlab platform.

  • Hankel/Toeplitz matrices and the static output feedback Stabilization Problem
    Mathematics of Control Signals and Systems, 2005
    Co-Authors: Alessandro Astolfi, Patrizio Colaneri
    Abstract:

    The static output feedback (SOF) Stabilization Problem for general linear, continuous-time and discrete-time systems is discussed. A few novel necessary and sufficient conditions are proposed, and a modified SOF Stabilization Problem with performance is studied. For multiple-input single-output (or single-input multiple-output) systems the relation with a class of Hankel matrices, and their inverses, in the continuous-time case and with a class of Toeplitz matrices, in the discrete-time case, is established. These relationships are used to construct conceptual numerical algorithms. Finally, it is shown that, in the continuous-time case, the Problem can be recast as a concave–convex programming Problem. A few worked out examples illustrate the underlying theory.

  • The static output feedback Stabilization Problem as a concave-convex programming Problem
    Proceedings of the 2004 American Control Conference, 2004
    Co-Authors: Alessandro Astolfi, Patrizio Colaneri
    Abstract:

    It is shown that the static output feedback Stabilization Problem for linear multi-input single-output (MISO) systems can be posed as a concave-convex programming Problem. This allows the potential design of minimization algorithms yielding a stabilizing static output feedback gain, if it exists, or showing that the Problem is not solvable at all.

Zhao Mingwang - One of the best experts on this subject based on the ideXlab platform.

  • A Numerical Algorithm for Simultaneous Stabilization Problem
    Control theory & applications, 1997
    Co-Authors: Zhao Mingwang
    Abstract:

    篒n this paper, the simultaneous Stabilization Problem for linear systems with different orders is transformed as a solving Problem of nonlinear inequalities, by using a sufficient criterion of polynomial stability. Then a quasi-Newton numeric algorithm for solving inequalities is presented firstly, and is applied to solving the simultaneous simulation Problem. Two examples show the effectiveness of the method.

H. Ozbay - One of the best experts on this subject based on the ideXlab platform.

  • On the strong Stabilization Problem and performance of stable /spl Hscr//sup /spl infin// controllers
    Proceedings of the 36th IEEE Conference on Decision and Control, 1
    Co-Authors: M. Zeren, H. Ozbay
    Abstract:

    A strong Stabilization Problem is considered for MIMO finite dimensional linear time invariant systems. It is shown that if an algebraic Riccati equation (ARE) has a positive semi-definite solution, then a strongly stabilizing controller can be constructed using state space techniques. This controller is of the same order as the plant. Moreover, under this sufficient condition, a finite dimensional characterization of a fairly large set of strongly stabilizing controllers is obtained. Using a similar ARE, the authors (1996) constructed a stable suboptimal /spl Hscr//sup /spl infin// controller of order 2n, where n is the order of the generalized plant. The /spl Hscr//sup /spl infin// performance level attained by this controller is studied here. An alternative stable /spl Hscr//sup /spl infin// controller design method is also discussed.

Alessandro Astolfi - One of the best experts on this subject based on the ideXlab platform.

  • Hankel/Toeplitz matrices and the static output feedback Stabilization Problem
    Mathematics of Control Signals and Systems, 2005
    Co-Authors: Alessandro Astolfi, Patrizio Colaneri
    Abstract:

    The static output feedback (SOF) Stabilization Problem for general linear, continuous-time and discrete-time systems is discussed. A few novel necessary and sufficient conditions are proposed, and a modified SOF Stabilization Problem with performance is studied. For multiple-input single-output (or single-input multiple-output) systems the relation with a class of Hankel matrices, and their inverses, in the continuous-time case and with a class of Toeplitz matrices, in the discrete-time case, is established. These relationships are used to construct conceptual numerical algorithms. Finally, it is shown that, in the continuous-time case, the Problem can be recast as a concave–convex programming Problem. A few worked out examples illustrate the underlying theory.

  • The static output feedback Stabilization Problem as a concave-convex programming Problem
    Proceedings of the 2004 American Control Conference, 2004
    Co-Authors: Alessandro Astolfi, Patrizio Colaneri
    Abstract:

    It is shown that the static output feedback Stabilization Problem for linear multi-input single-output (MISO) systems can be posed as a concave-convex programming Problem. This allows the potential design of minimization algorithms yielding a stabilizing static output feedback gain, if it exists, or showing that the Problem is not solvable at all.

W.-y. Yan - One of the best experts on this subject based on the ideXlab platform.

  • Gradient flow approach to LQ cost improvement for simultaneous Stabilization Problem
    Optimal Control Applications and Methods, 1996
    Co-Authors: Victor Sreeram, K.l. Teo, Wanquan Liu, W.-y. Yan
    Abstract:

    In this paper we consider LQ cost optimization for the simultaneous Stabilization Problem. The objective is to find a single simultaneously stabilizing feedback gain matrix such that all closed-loop systems exhibit good transient behaviour. The cost function used is a quadratic function of the system states and the control vector. This paper proposes to seek an optimization solution by solving an ordinary differential equation which is a gradient flow associated with the cost function. Two examples are presented to illustrate the effectiveness of the proposed procedure.

  • A gradient flow approach to simultaneous Stabilization Problem
    Proceedings of 1994 33rd IEEE Conference on Decision and Control, 1
    Co-Authors: Victor Sreeram, K.l. Teo, W.-y. Yan
    Abstract:

    In this paper, the Problem of simultaneous stabilizing optimally a set of linear time invariants systems is considered. The objective is to find a single feedback gain matrix such that: 1) all systems involved are simultaneously stabilized; and 2) all closed-loop systems exhibit good transient behaviour. This objective is achieved by posing the simultaneous Stabilization Problem as an optimal control Problem. The performance index used is a quadratic function of the system states and the control vector. In this paper, assuming that an initial solution to the simultaneous Stabilization Problem is known, an optimum solution in LQ sense is obtained using gradient flow methods. >

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