Stability and Stabilization of Nonlinear Stochastic Systems With Synchronous and Asynchronous Switching Parameters to the States
本文研究了非线性混合随机系统的稳定性与镇定问题，提出了同步和异步切换参数的概念，建立了稳定性判据和镇定方法，并通过数值例子验证了方法的有效性。
This article is concerned with the stability and stabilization of nonlinear hybrid stochastic systems. First, the concepts of synchronous and asynchronous switching parameters to the system states are proposed for a generalization of the asynchronous control. As preliminaries, a hybrid nonlinear differential inequality is established for coping with the synchronous models, and the [Formula: see text]-continuity of the system parameters driven by Markov chains is established for coping with the asynchronous models by the attribute of Markov chains for less conservativeness. Second, stability criteria with moment exponential estimates are established for two kinds of system models under the nonlinear growth condition. Third, the stabilization problem is illustrated based on the stability criteria and Riccati like matrix equations. A corollary is given to improve some stability theorems obtained in the related literature. New initial condition is formally proposed and explained for the nonlinear stochastic systems. Finally, a numerical example with simulation is proposed to illustrate the method, verify the conclusions of this article, and show the superiority of this work.