新的时变时滞不确定系统的稳定性判据

A New Method of Stability Criterion for Uncertain Systems with Time-varying Delay

研究带有时变有界的不稳定时滞系统的稳定性问题.通过运用Lyapunov-Krasovskii稳定性理论、合理建立Lyapunov-Krasovskii函数,结合积分不等式引理和交互式凸组合方法,减少不确定时变时滞系统相关判据的决策变量,给出了系统是渐近稳定的充分条件.所得结论采用线性矩阵不等式表示.数值例子验证了该方法的有效性.

The stability problem concerning uncertain time and varying delay systems with time-varying bound is studied .By applying Lyapunov-Krasovskii stability theory ,constructing the Lya-punov-Krasovskii functions properly and combining integral inequality lemma with reciprocally convex method ,which is a way of reducing the number of decision variables ,the sufficient conditions for as-ymptotic stability of the systems are given .The resulting criterion is based on linear matrix inequalities （LMIs） .A numerical example is given to show the effectiveness of the method .