Abstract
This paper addresses the robust stability for a class of linear discrete-time stochastic systems with convex polytopic uncertainties. The system to be considered is subject to both interval time-varying delays and convex polytopic type uncertainties. Based on the augmented parameter-dependent Lyapunov-Krasovskii functional, new delay-dependent conditions for the robust stability are established in terms of linear matrix inequalities. An application to robust stabilization of linear discrete-time stochastic control systems is given. Numerical examples are included to illustrate the effectiveness of our results.
Highlights
In the past decades, the problem of stability for neutral differential systems, which have delays in both its state and the derivatives of its states, has been widely investigated by many researchers
This paper addresses the robust stability for a class of linear discrete-time stochastic systems with convex polytopic uncertainties
Based on the augmented parameter-dependent Lyapunov-Krasovskii functional, new delay-dependent conditions for the robust stability are established in terms of linear matrix inequalities
Summary
The problem of stability for neutral differential systems, which have delays in both its state and the derivatives of its states, has been widely investigated by many researchers. To the best of our knowledge, the stability and stabilization of linear discrete-time stochastic systems with convex polytopic uncertainties, nondifferentiable time-varying delays has not been fully studied yet (see, e.g., [1, 3–11, 13–36] and the references therein), which are important in both theories and applications.
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