离散双切换线性正系统的L1增益性能分析

Analysis of L1 Gain Performance of Discrete Dual Switched Linear Positive Systems

离散时间双切换线性正系统是同时受到确定切换信号和Markov随机切换信号共同影响的系统。鲁棒稳定以及扰动抑制问题是研究混杂系统稳定性的重要问题,但双切换正系统的扰动抑制问题研究较少。基于此研究背景,提出了新型的切换系统——具有指数不确定性的离散时间双切换线性正系统(DDSLPS),通过构建Co-positive Lyapunov能量衰减函数,利用线性编程(LP)得到确保DDSLPS在持续驻留时间(PDT)约束下系统满足鲁棒指数几乎处处稳定(Robust-EAS)的充分条件。另外,将此方法推广到DDSLPS的L1增益分析中,得到闭环系统在鲁棒指数几乎处处稳定下满足L1性能指标x的充分条件。利用Matlab数值仿真,验证了所用方法的有效性和所得结果的正确性。

Discrete-time dual-switched linear positive systems are affected by both deterministic switching signals and Markov random switching signals.Robust stability and disturbance suppression are important problems in the study of the stability of hybrid systems,but the disturbance suppression of dual-switched positive systems is rarely studied.Based on this research background,a novel switching system,discrete-time dual-switched linear positive system(DDSLPS)with exponential uncertainty is proposed.By constructing Co-positive Lyapunov energy decay function,by using linear programming(LP),a sufficient condition is obtained to ensure Robust-exponential almost-sure stability(Robust-EAS)of DDSLPS under persistent dwell-time(PDT)constraints.In addition,this method is extended to L1 gain analysis of DDSLPS,and a sufficient condition is obtained that the closed-loop system satisfies L1 performance index x when the robust index is almost everywhere stable.Matlab numerical simulation is used to verify the effectiveness of the method and the correctness of the obtained result.