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Robust H∞ control for a class of uncertain neutral systems with both state and control input time-varying delays via a unified LMI optimization approach

Chen J. D., Yang C. D., Lin K. J., Lien C. H.

Control and Cybernetics

2008

Vol. 37, no 3

517-530

The robust H∞ control problem is considered for a class of uncertain neutral system involving both state and control input time-varying delays. The uncertainties under consideration are nonlinear time-varying parameter perturbations. The methodology is based on the Lyapunov functional combined with a unified LMI approach, and a new delay-dependent criterion is proposed to guarantee the stabilization and disturbance attenuation of systems. Moreover, a convex optimization approach is used to solve the robust H∞ control disturbance attenuation problem. Finally, a numerical example is illustrated to show the validity of this paper. The simulation results reveal significant improvement over the recent results.

Stability criteria for large-scale time-delay systems; the LMI approach and the Genetic Algorithms

Chen J.- D.

Control and Cybernetics

2006

Vol. 35, no 2

291-301

This paper addresses the asymptotic stability analysis problem for a class of linear large-scale systems with time delay in the state of each subsystem as well as in the interconnections. Based on the Lyapunov stability theory, a delay-dependent criterion for stability analysis of the systems is derived in terms of a linear matrix inequality (LMI). Finally, a numerical example is given to demonstrate the validity of the proposed result.

Stability of nominally stable uncertain singularly perturbed systems with multiple time delays

Chen C., Pan S., Hsieh J.

Control and Cybernetics

2002

Vol. 31, no 1

5-16

In this paper, the robust asymptotic stability problem for a class of nominally stable uncertain singularly perturbed systems with multiple non-commensurate time delays is considered. A delay-dependent criterion is first proposed in this paper to guarantee robust asymptotic stability of the system under consideration. Based on this result, the range of allowable bounds of the perturbation matrices preserving the closed-loop stability can easily be found. Moreower, a simple criterion is also proposed to guarantee asymptotic, stability of the nominal system. Furthermore, a simple estimation of the stability bound epsilon* is proposed such that the nominal system is asymptotically stable for epsilon [belongs to](0,epsilon*). It can be seen that the stability bound proposed in this paper is less conservative than that presented in recent research. Finally, a numerical example is provided to illustrate our main results.