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针对一类切换广义时滞系统的稳定性问题进行了研究.提出了一种新的研究切换广义时滞系统的多Lyapunov泛函,利用Lyapunov稳定性理论和线性矩阵不等式工具,通过引入适当的自由权矩阵,在设定的切换律下,得到了基于严格线性矩阵不等式表示的切换广义时滞系统的时滞相关稳定性条件.进一步通过建立一个具有线性矩阵不等式约束的凸优化问题,得到了保证切换广义时滞系统渐近稳定的最大可允许时滞上界,最后的数值算例表明了该方法的有效性.
In this paper, we study the stability of a class of switched generalized time-delay systems. A new multi-Lyapunov functional for switched generalized systems with time-delay is proposed. By using Lyapunov stability theory and linear matrix inequality tools, Under the set switching law, the delay-dependent stability conditions for switched generalized time-delay systems based on strict linear matrix inequalities are obtained. By further establishing a convex optimization problem with linear matrix inequality constraints, we obtain the guaranteed The maximum allowable upper bound of delay for switching asymptotic stability of a generalized time-delay system is given. Finally, a numerical example shows the effectiveness of the proposed method.