Stability and stabilization analysis of periodic switching stochastic systems based on Lyapunov function with continuous time-varying matrix polynomials

In this paper, a Lyapunov function with continuous time-varying Lyapunov matrix polynomials is constructed to ensure the exponential stability in mean square of a periodic switched linear stochastic system, where the Lyapunov matrix of this Lyapunov function is no longer a constant matrix, but a continuous time-varying matrix polynomial. Then, based on this stability study, we design an aperiodic intermittent control for unstable periodic switching stochastic systems to solve the influence of unstable subsystems and switching rules on stability, and the corresponding control gains are continuous time-varying matrix polynomial. Finally, an example is demonstrated to illustrate the effectiveness of the proposed control strategy.