一类不确定变时滞切换系统的非脆弱H_(∞)控制

Non-fragile H_(∞)control for a class of uncertain switched systems with variable delay

讨论了一类不确定变时滞切换系统在构造的切换律下的非脆弱H_(∞)控制问题。首先,在同时限定时滞上界和时滞导数上界的条件下利用单李雅普诺夫函数方法、凸组合技术,构造李雅普诺夫泛函和其对应的切换规则;然后,利用不等式引理对求导后的李雅普诺夫泛函进行不等式放缩进而消除不等式中的时变时滞项,再引入J函数得到满足H_(∞)性能指标γ的非线性矩阵不等式,并利用Schur补引理将非线性矩阵不等式转化为线性矩阵不等式;最后,给出由2个子系统构成的一个切换系统,利用LMI工具箱进行数值例子仿真说明了定理的有效性和实用性。最终得出了一类不确定变时滞切换系统存在非脆弱状态反馈控制器且满足H_(∞)性能指标γ的充分条件。

In this paper,the non-fragile H_(∞) control problem of a class of uncertain switching systems with variable time delay under the constructed switching law is discussed.First,under the condition that both the upper bound of the delay and the upper bound of the derivative of the delay are defined at the same time,the single Lyapunov function method and the convex combination technique are used to construct the Lyapunov functional and its corresponding switching rules;Secondly,the inequality lemma is used to scale the inequality of the derived Lyapunov functional to eliminate the time-varying delay term in the inequality,and then a function J is introduced to obtain a nonlinear matrix inequality that satisfies the H_(∞) performance indexγ,and Schur complement lemma is used to convert nonlinear matrix inequalities into linear matrix inequalities;Finally,a switching system consisting of two subsystems is given,and numerical examples are simulated using LMI toolbox to illustrate the validity and practicability of the theorem.Eventually,the sufficient conditions for the existence of a non fragile state feedback controller and satisfying the H_(∞) performance indexγof a class of uncertain switched systems with time-varying delay are obtained.