New Results on Robust Stability and Stabilization of Linear Discrete-Time Stochastic Systems with Convex Polytopic Uncertainties

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.

Stability and stabilization of fractional-order linear systems with convex polytopic uncertainties

This paper considers the problems of robust stability and stabilization for a class of fractional-order linear time-invariant systems with convex polytopic uncertainties. The stability condition of the fractional-order linear time-invariant systems without uncertainties is extended by introducing a new matrix variable. The new extended stability condition is linear with respect to the new matrix variable and exhibits a kind of decoupling between the positive definite matrix and the system matrix. Based on the new extended stability condition, sufficient conditions for the above robust stability and stabilization problems are established in terms of linear matrix inequalities by using parameter-dependent positive definite matrices. Finally, numerical examples are provided to illustrate the proposed results.

A SWITCHING RULE FOR THE ASYMPTOTIC STABILITY OF DISCRETE-TIME SYSTEMS WITH CONVEX POLYTOPIC UNCERTAINTIES

This paper addresses the stability for a class of linear delay-difference equations with interval time-varying delays. Based on the parameter-dependent Lyapunov–Krasovskii functional, new delay-dependent conditions for the stability are established in terms of linear matrix inequalities. Numerical examples are included to illustrate the effectiveness of our results.