不确定离散时滞分段系统的广义H_2弹性控制

General H_2 Resilient Control for Uncertain Discrete Time-delay Piecewise Systems

针对一类不确定离散时滞分段系统,研究了广义H_∞稳定性分析和带有时滞的状态反馈弹性控制器设计问题。通过构造适当的离散分段二次李亚普诺夫函数,利用分段二次李亚普诺夫稳定性理论,给出了对于所有的容许参数不确定性,闭环系统是广义H=∞稳定的充分条件;在此基础上,基于线性矩阵不等式(LMI)处理方法,提出了带有时滞的状态反馈弹性控制器增益阵的设计方案。仿真实例验证了所提方法的有效性。

According to a uncertain discrete time-delay piecewisc systems, the general H2 stability analysis and time-delay resilient controller design problems are studied. General H2 stability sufficient conditions of the closed-loop system for all admissible uncertainties are derived from constructing an appropriate discrete piecewise quadratic Lyapunov function. Based on linear matrix inequality（LMI）method, the design scheme for resilient controller is also provided. A numerical example shows the feasibility and effectiveness of the proposed method.