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Linear Time-delay Systems (linear + time-delay_system)

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Selected Abstracts

Strong stability radii of positive linear time-delay systems

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 10 2005
Pham Huu Anh NgocArticle first published online: 18 MAY 200
Abstract In this paper, we study robustness of the strong delay-independent stability of linear time-delay systems under multi-perturbation and affine perturbation of coefficient matrices via the concept of strong delay - independent stability radius (shortly, strong stability radius). We prove that for class of positive time-delay systems, complex and real strong stability radii of positive linear time-delay systems under multi-perturbations (or affine perturbations) coincide and they are computed via simple formulae. Apart from that, we derive solution of a global optimization problem associated with the problem of computing of the strong stability radii of a positive linear time-delay system. An example is given to illustrate the obtained results. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Delay-dependent anti-windup strategy for linear systems with saturating inputs and delayed outputs

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 7 2004
S. Tarbouriech
Abstract This paper addresses the problem of the determination of stability regions for linear systems with delayed outputs and subject to input saturation, through anti-windup strategies. A method for synthesizing anti-windup gains aiming at maximizing a region of admissible states, for which the closed-loop asymptotic stability and the given controlled output constraints are respected, is proposed. Based on the modelling of the closed-loop system resulting from the controller plus the anti-windup loop as a linear time-delay system with a dead-zone nonlinearity, constructive delay-dependent stability conditions are formulated by using both quadratic and Lure Lyapunov,Krasovskii functionals. Numerical procedures based on the solution of some convex optimization problems with LMI constraints are proposed for computing the anti-windup gain that leads to the maximization of an associated stability region. The effectiveness of the proposed technique is illustrated by some numerical examples. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Stability and H, performance of multiple-delay systems with successive delay components

INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 8 2010
Ge Guo
Abstract This paper presents a new model for linear time-delay systems with multiple delayed states where each delay contains finite number of successive components with different time-varying properties, referred to as multiple-delay system with successive time-varying delay components (MDSSTDCs). General stability result and H, performance conditions, under which the MDSSTDCs are asymptotically stable with certain H, disturbance attenuation level, are derived by exploiting a general Lyapunov,Krasovskii functional and by making use of novel techniques for time-delay systems. The result is applied to two special types of time-delay systems frequently used in engineering applications and corresponding conditions for stability and H, performance are obtained. Copyright © 2010 John Wiley & Sons, Ltd. [source]

Strong stability radii of positive linear time-delay systems

New results for the analysis of linear systems with time-invariant delays

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 12 2003
Jianrong Zhang
Abstract This paper presents a comparison system approach for the analysis of stability and ,, performance of linear time-invariant systems with unknown delays. The comparison system is developed by replacing the delay elements with certain parameter-dependent Padé approximations. It is shown using the special properties of the Padé approximation to e,s that the value sets of these approximations provide outer and inner coverings for that of each delay element and that the robust stability of the outer covering system is a sufficient condition for the stability of the original time delay system. The inner covering system, in turn, is used to provide an upper bound on the degree of conservatism of the delay margin established by the sufficient condition. This upper bound is dependent only upon the Padé approximation order and may be made arbitrarily small. In the single delay case, the delay margin can be calculated explicitly without incurring any additional conservatism. In the general case, this condition can be reduced with some (typically small) conservatism to finite-dimensional LMIs. Finally, this approach is also extended to the analysis of ,, performance for linear time-delay systems with an exogenous disturbance. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Rejection of persistent-bounded disturbances in linear time-delay systems by output-feedback

OPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 4 2010
Magdi S. Mahmoud
Abstract In this paper, the problem of persistent-bounded disturbance rejection of linear continuous-time systems with time-varying delays is investigated using the tools of invariant set analysis and Lyapunov-function methodology. We derive less conservative sufficient conditions on robust attractor for time-delay systems in terms of strict linear matrix inequalities (LMIs) to guarantee the desired ,1 -performance. A robust output-feedback controller is designed and the associated gain is determined using strict LMIs. The developed results are tested on two representative time-delay examples. Copyright © 2009 John Wiley & Sons, Ltd. [source]