不确定广义时滞系统的时滞相关鲁棒镇定新判据

New criteria on delay-dependent robust stabilization for uncertain singular time-delay systems

针对线性不确定广义时滞系统,给出了新的时滞相关鲁棒稳定性判据和镇定方法.假定参数是可能时变的范数有界不确定,通过选取一个新的Lyapunov-Krasovskii泛函将整个时滞区间分为2段.每段区间上定义了不同的能量函数,给出了状态反馈控制器设计算法,保证相应的闭环系统对所有容许的不确定性参数是正则、因果和鲁棒稳定的.新的时滞相关鲁棒稳定性判据由线性矩阵不等式表示,判据所给出的条件保守性小于已有的结论.数值算例进一步证明了该结论的有效性.

Some new results of delay-dependent robust stability and stabilization for uncertain linear singular time-delay systems are presented. The parameter uncertainty is assumed to be norm-bounded and possibly time-varying. By using a new Lyapunov-Krasovskii functional which splits the whole delay interval into two subintervals and defines a different energy function on each subinterval, a suitable state feedback control law is obtained, which guarantees the singular time-delay system to be regular, impulse free and robustly stable for all admissible uncertainties. The new delay-dependent criteria are formulated in terms of linear matrix inequalities （LMIs）. Numerical example is given to show the effectiveness and less conservativeness of the proposed method.