Chien-Hua Lee

D-stability analysis for discrete systems with a time delay

This paper first discusses the D-pole placement problem of discrete time-delay systems. Some criteria are proposed to ensure that all the closed-loop eigenvalues of discrete systems with a time delay are located inside a specific disk D(α, r) centered at (α, 0) with radius r. Then, several sufficient conditions for guaranteeing the D-stability of discrete time-delay systems subjected to parametric perturbations are presented. Both unstructured and highly structured parametric perturbations are considered. By these sufficient conditions, the tolerable parametric perturbation bounds that ensure all the closed-loop poles of discrete time-delay perturbed systems to remain inside the desired disk D(α, r) can be estimated. Finally, illustrative examples are given for demonstration.

A new approach for the robust stability of perturbed systems with a class of noncommensurate time delays

In this paper, based on the Lyapunov stability theorem, matrix measure, and norm inequalities, a new approach for the robust stability of perturbed systems with a class of noncommensurate time delays is presented. Two classes of linear parametric perturbations are treated: (1) unstructured; and (2) highly structured perturbations. Several concise sufficient conditions, delay-dependent or delay-independent, are proposed to guarantee the asymptotic stability and positive stability degree of the perturbed multiple time-delay systems. Finally, two numerical examples are given to demonstrate the applications of these quantitative results. >

On the robust stability for continuous large‐scale uncertain systems with time delays in interconnections

Abstract In this paper, the robust stability testing problem is addressed for continuous large‐scale uncertain systems with time delays in interconnections. Three classes of system uncertainties are examined: (i) nonlinear time‐varying uncertainties; (ii) linear unstructured uncertainties; and (iii) linear highly structured uncertainties. By applying the Lyapunov stability theorem, several new delay‐independent sufficient conditions are established in terms of concise inequalities, which can maintain the stability of continuous large‐scale uncertain time‐delay systems. Finally, illustrative examples are given to demonstrate the application of the results presented here.

On the robustness of stability for uncertain time-delay systems

Abstract Based on the Lyapunov stability theorem associated with induced norm of matrix and matrix measure techniques, this paper addresses the robust stability analysis for linear time-delay systems with uncertainties. Several new criteria, expressed by concise inequalities, are presented to guarantee the robust stability and stability with a specified decaying rate for the above systems. Both nonlinear norm-bounded and highly structured parametric uncertainties are discussed. Finally, the superiority of the proposed results is demonstrated in the illustrative examples by comparing with those available in the literature

New results for the stability of uncertain time-delay systems

In this paper, based on the Lyapunov stability theorem associated with matrix measure techniques, some new delay-independent criteria for asymptotic stability of linear perturbed time-delay systems are proposed. Furthermore, the stability degree testing problem of the above systems is also investigated. From the given examples, we demonstrate the superiority of these quantitative results by comparing them with other approaches presented in the literature

Robustness of D-stability for discrete large-scale uncertain systems

Based on Lyapunov stability theory associated with transformation techniques, the D-stability robustness problem is first discussed for discrete large-scale systems subjected to interconnections and perturbations. Three classes of perturbation are treated: (1) unstructured parametric perturbations; (2) highly structured parametric perturbations; and (3) nonlinear perturbations. If all the eigenvalues of each nominal subsystem are located inside the specified discs D i (α i , r i ), respectively, sufficient conditions for D-stability are presented to guarantee that all the eigenvalues of each perturbed subsystem remain inside the same discs

On the estimation of eigenvalue regions for discrete time-delay systems with a class of highly structured perturbations

By means of norm,M-matrix, and matrix measure techniques, this paper estimates several restricted regions in the complex plane in which all eigenvalues of a class of discrete time-delay systems subjected to highly structured parametric perturbations are located. Both the stability and the instability conditions for these systems are also investigated via the proposed schemes. Two numerical examples are given to verify the correctness and demonstrate the applicability of the quantitative results.

A new robust stability test for a class of linear systems with uncertainties and multiple time delays

Abstract This paper addresses the robust stability problem for the linear multiple time- delay system subjected to nonlinear time-varying perturbations. By means of complex Lyapunov equations, norm and matrix measure inequalities, a new approach is proposed to solve such problems. Several new criteria, delay-dependent or delay-independent, are derived to guarantee the asymptotic stability of the uncertain multiple time-delay systems. The 7stability decaying rate of such systems is also investigated. The main feature of the developed results is that it is not necessary to solve any troublesome Lyapunov equation even though the Lyapunov stability test is used. Furthermore, the generality of these results is assured by comparing with those presented in the literature.

A Riccati equation approach to the robust memoryless stabilization of discrete time-delay systems

Abstract By applying a Riccati equation approach, this paper presents a new memoryless feedback controller for stabilizing a class of discrete systems with an unknown state delay. By evaluating the tolerable system uncertainty bounds, the robustness of this memoryless feedback controller is also investigated.

On the robustness of stability for uncertain large-scale systems subjected to multiple time delays

The robustness problem of stability for large-scale uncertain systems with a class of multiple time delays is addressed in this paper. By applying the complex Lyapunov stability theorem, the matrix measure techniques, and norm inequalities, a new approach for solving a general case of the above problem is proposed. Several robust stability conditions, delay-dependent or delay-independent, are derived to guarantee the asymptotic stability and exponential stability of the uncertain large-scale time-delay systems. Moreover, these obtained results can also be applied to the stabilization design.