Time Delay System Stabilisation

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Author Index
A B C D E F G H I
J K L M N O P Q R
S T U V W X Y Z

Controller Design for Time-Delay Systems Using Discretized Lyapunov Functional Approach

Authors:

Keqin Gu, Qing-Long Han,

Volume: 1, Page 2793 Paper number 47

Abstract:

This paper investigates the controller synthesis of uncertain linear time-delay systems. Stabilizability criteria are derived based on a discretized Lyapunov functional approach. A new controller design method is developed. Numerical examples show that the results using the proposed method are less conservative than some existing ones.

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Delay Sensitivity Of Quadratic Controllers: A Singular Perturbation Approach

Authors:

Papa Momar Ndiaye, Michel Sorine,

Volume: 1, Page 2799 Paper number 13

Abstract:

We study the variations of the quadratic performance associated to a linear differential system of retarded type for small values of the delays. From an interpretation of delays as singular perturbations of abstract evolution operators, we revisit the usual theory of representation and optimal control of retarded systems. This leads to a new parameterization of associated Riccati operators for which insight is gained in the dependence on the delays. This explicit parameterization of Riccati operators by the delays enables us to prove differentiability at zero for performance viewed as a function of the delays, in the LQ-optimal or H-infinity sub-optimal control. The gradient is explicitly computed in terms of the non-negative solution of the finite dimensional Riccati equation associated to the non-delay control problem.

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An Integral Inequality In The Stability Problem Of Time-Delay Systems

Authors:

Keqin Gu,

Volume: 1, Page 2805 Paper number 1674

Abstract:

An integral inequality is derived, and applied to the stability problem of time-delay systems using discretized Lyapunov functional formulation. As the result, a simpler stability criterion is derived.

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Delay Effects on Static Output Feedback Stabilization

Authors:

Silviu-Iulian Niculescu, Chaouki T. Abdallah,

Volume: 1, Page 2811 Paper number 1485

Abstract:

This paper addresses conditions for characterizing static output feedback controllers including delays for some proper (finite-dimensional) transfer functions. The interest of such study is in controlling systems which can not be stabilized by the classical, nondelayed static output feedback, and its difficulty lies in computing delay intervals guaranteeing closed-loop stability, since stability switches/reversals may occur for the same (matrix) gain if the delay is seen as a 'free' (design) parameter. The derived conditions are expressed in terms of some appropriate matrix pencils or MIMO Nyquist tests. Illustrative examples are also presented.

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Invertibility and Inversion for Systems over Rings and Applications to Delay-Differential Systems

Authors:

Giuseppe L. Conte, Anna Maria Perdon,

Volume: 1, Page 2817 Paper number 2038

Abstract:

The notion of invertibility for systems with coefficients in a ring is investigate. An algebraic notion of relative degree is introduced and used to characterize the invertibility of a SISO system, while a geometric characterization of relative degree is given for the MIMO case. Application to the study of delay differential systems are presented.

CD002038.PDF (From Author)

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Input-Output Passive Framework for Delay Systems

Authors:

Vladimir Rasvan, Silviu-Iulian Niculescu, Rogelio Lozano,

Volume: 1, Page 2823 Paper number 8016

Abstract:

Multivariable linear systems with several delays are considered. Delays are allowed in the state as well as in the input or the output. Passivity and dissipativity of such systems are considered both in the input-output and state space framework in connection with hyperstability. In the input-output framework necessary and sufficient conditions of passivity and hyperstability of delay systems are given in the language of positive real functions. Furthermore, necessary and st@cient conditions for positive realness are derived for a class of meromorphic functions describing delay systems.

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Stability Condition of Distributed Delay Systems Based on the Analytic Solution of Lyapunov Functional Equations

Authors:

Young Soo Suh,

Volume: 1, Page 2829 Paper number 9149

Abstract:

Analytic solution of Lyapunov functional equations of distributed delay systems is derived. The analytic solution is computed using a matrix exponential function, while conventional computation has been relied on numerical approximations. Based on the analytic solution, a stability condition for distributed delay systems with unknown but bounded constant delay is proposed.

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