时滞不确定随机系统的时滞相关稳定与镇定判据

Delay-dependent Stability and Stabilization Criteria for Uncertain Stochastic Systems with Time-varying Delays

将自由权矩阵思想推广到一类时滞不确定随机系统中,研究了其时滞相关稳定与镇定问题.通过构造新的Lyapunov函数,引入适当的自由权矩阵,推导出系统渐近稳定的时滞相关的充分条件,并构造了保证系统渐近稳定的时滞相关状态反馈控制器.所得结果完全基于线性矩阵不等式的形式给出,不需要对原系统模型进行变换.仿真算例验证了方法的可行性.

The idea of free-weighting matrices is extended to a class of stochastic systems with time-varying delays,and its delay-dependent stability and stabilization are considered.By establishing a new Lyapunov function and introducing appropriate free-weighting matrices,a sufficient delay-dependent condition is proposed for the asymptotic stability of such a system.Moreover,the stability criteria is used to design the delay-dependent state-feedback controller,which guarantee that the system is robust asymptotically stable.The result accords with the form of linear matrix inequalities completely and the model transformation is unnecessary.The examples are given to illustrate the effectiveness of the proposed method.