Abstract
This paper is concerned with the problem of robust exponential stability for linear parameter-dependent (LPD) neutral systems with mixed time-varying delays and nonlinear perturbations. Based on a new parameter-dependent Lyapunov-Krasovskii functional, Leibniz-Newton formula, decomposition technique of coefficient matrix, free-weighting matrices, Cauchy’s inequality, modified version of Jensen’s inequality, model transformation, and linear matrix inequality technique, new delay-dependent robust exponential stability criteria are established in terms of linear matrix inequalities (LMIs). Numerical examples are given to show the effectiveness and less conservativeness of the proposed methods.
Highlights
Over the past decades, the problem of stability for neutral differential systems, which have delays in both their state and the derivatives of their states, has been widely investigated by many researchers, especially in the last decade
The results have been obtained for robust stability for linear parameter-dependent (LPD) systems in which time-delay occurs in state variable; for example, [17, 18] presented sufficient conditions for robust Journal of Applied Mathematics stability of LPD discrete-time systems with delays
This paper investigates the robust exponential stability analysis for LPD neutral systems with mixed time-varying delays and nonlinear perturbations
Summary
The problem of stability for neutral differential systems, which have delays in both their state and the derivatives of their states, has been widely investigated by many researchers, especially in the last decade. Many researchers have studied the stability problem for neutral systems with time-varying delays and nonlinear perturbations have appeared [29, 31]. The results have been obtained for robust stability for LPD systems in which time-delay occurs in state variable; for example, [17, 18] presented sufficient conditions for robust. This paper investigates the robust exponential stability analysis for LPD neutral systems with mixed time-varying delays and nonlinear perturbations. Based on combination of Leibniz-Newton formula, free-weighting matrices, Cauchy’s inequality, modified version of Jensen’s inequality, decomposition technique of coefficient matrix, the use of suitable parameter-dependent Lyapunov-Krasovskii functional, model transformation, and linear matrix inequality technique, new delay-dependent robust exponential stability criteria for these systems will be obtained in terms of LMIs. numerical examples will be given to show the effectiveness of the obtained results
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