具有随机逆动态的马尔可夫切换随机低阶非线性系统的有限时间镇定  

Finite-Time Stabilization of Markovian Switched Stochastic Low-Order Nonlinear Systems with Stochastic Inverse Dynamics

作　　者：张雪 赵桂华 

机构地区：[1]上海理工大学理学院,上海

出　　处：《应用数学进展》2023年第4期1487-1495,共9页Advances in Applied Mathematics

摘　　要：本文研究了一类具有马尔可夫切换和随机逆动态的随机低阶非线性系统的有限时间镇定问题。我们首先在弱解的框架下给出了有限时间稳定性理论,然后结合李雅普诺夫函数和加幂积分器技术构造了状态反馈控制器。证明了具有马尔可夫开关的随机低阶非线性系统的平凡弱解是全局有限时间稳定的。最后,通过仿真实例验证了所提设计方法的有效性。In this paper, we investigate the finite-time stabilization of a class of stochastic low-order nonlinear systems with Markovian switching and stochastic inverse dynamics. We first present the finite-time stability theory under the framework of weak solutions. Then, combining the Lyapunov function and adding a power integrator technique, a state feedback controller is designed to guarantee glob-al finite-time stability in probability of stochastic low-order nonlinear systems with finite-time sto-chastic inverse dynamics. Finally, the effectiveness of the proposed design method is verified by a simulation example.

关 键 词：有限时间稳定 马尔可夫切换 随机逆动态 随机非线性系统 状态反馈控制器 

分 类 号：O17[理学—数学]