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This article is concerned with mean square robust stability of stochastic switched discrete time-delay systems with convex polytopic uncertainties.

This article studies mean square robust stability problem for stochastic switched linear discrete systems with convex polytopic uncertainties with interval time-varying delays.

By using improved Lyapunov-Krasovskii functionals combined with LMIs technique, we propose new criteria for the mean square robust stability of the system.

Second, the approach allows us to design the switching rule for mean square robust stability in terms of LMIs, which can be solvable by utilizing Matlab's LMI Control Toolbox available in the literature to date.

Switching rule for the mean square robust stability is presented in Section 3. Numerical example is provided to illustrate the theoretical results in Section 4, and the conclusions are drawn in Section 5.

Based on the discrete Lyapunov functional, a switching rule for the mean square robust stability for the stochastic switched system with convex polytopic uncertainties is designed via linear matrix inequalities.

In practical robust design applications, a second-order polynomial model is adequate to accommodate the curvature of process mean and variance functions, thus mean-squared robust design models, frequently used by many researchers, would contain fourth-order terms.

In this work we derive necessary and sufficient conditions for robust mean square stability of discrete-time time-inhomogeneous Markov jump linear systems (MJLSs) affected by polytopic uncertainties on transition probabilities and bounded disturbances.

By using the Lyapunov functional method and the linear matrix inequality technology, sufficient conditions for the robust mean square stable (RMSS) of the NCSs with an H∞ norm bound γ are obtained.

The dynamics of the filtering error systems are guaranteed to be robust stochastically mean square asymptotically stable, while achieving a prescribed stochastic robust H∞ performance level.

end{aligned} Hence (18) is robust exponentially mean square stable.