一类不确定时滞线性切换系统的鲁棒H∞控制

摘要

不确定因素和时滞是现实控制系统中经常存在的问题，在切换系统中，这种问题尤为突出。而状态反馈和鲁棒控制的加入便有效地解决了这些情况对系统稳定性的影响。本文针对一类存在状态时滞和不确定因素的线性切换系统的状态反馈控制问题，研究在公共 Lyapunov函数下，满足特定鲁棒 H∞性能时，状态反馈控制器存在的条件和求解方法。运用 Schur补引理，得出相应的不等式和定理，并进一步将其转化为线性矩阵不等式(LMIs)，利用 MATLAB进行仿真证明了结论的有效性。%This paper focused on a class of linear switched systems containing state-delay and two uncertain factors of the state feedback control problem.Under the common Lyapunov function that meets certain robust H∞ performance,the existence condition of state feedback controller and the corresponding solving method were studied,the corresponding ine-quality and theorems were obtained by using Schur complement lemma,and were transformed into linear matrix inequality (LMIs).The MATLAB simulation prove the validity of the conclusion.