具有异步控制器的离散马尔可夫跳变Lur’e系统的稳定性和e_2增益性能分析

Stability and e_2-gain analysis for discrete-time Markov jump Lur'e aystems with asynchronous controller

本文研究了一类具有异步控制器的离散马尔可夫Lur’e跳变系统的稳定性及e_2增益性能.通过引入隐马尔可夫模型(HHM)来描述所设计的控制器和原始系统之间出现的异步现象.利用线性矩阵不等式(LMI)方法分析了闭环系统的稳定性和e_2增益性能.然后提出了一个充分条件使得闭环系统随机稳定,并使得从扰动到系统输出的e_2增益达到最小.同时,通过求解给定条件来设计一个由线性状态反馈和扇形有界非线性输出反馈组成的异步控制器.最后,给出了一个数值仿真例子来验证所提方法的有效性.

This paper is concerned with the stability and e2-gain performance for a class of discrete-time Lur’e systems with an asynchronous controller.A hidden Markov model( HHM) is introduced to describe the asynchronization that appears between the designed controller and the original system.The linear matrix inequality( LMI) approach is utilized to analyze the stability of the closed-loop system and e2-gain performance.Then a sufficient condition is proposed to guarantee the stochastic stability of the closed-loop system,and to minimize the obtained e2-gain from the disturbance to output. Thus,an asynchronous controller consisting of both linear state feedback and conebounded nonlinear output feedback can be designed by solving the given conditions.A simulation example is given to demonstrate the effectiveness of the proposed method.