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研究一类由任意有限多个具有参数不确定性和状态时滞的奇异子系统组成的切换系统的状态反馈鲁棒H∞控制问题。利用Lyapunov函数方法和凸组合技术,给出由矩阵不等式表示的控制器存在的充分条件,并设计了相应的子控制器和切换规则。采用变量替代方法,将该矩阵不等式转化为一组线性矩阵不等式(LMIs)。最后给出电力系统中一个求解状态反馈控制器增益矩阵的仿真算例证明结论的有效性。研究结果表明,通过切换,闭环系统在整个状态空间上的每个点都满足鲁棒H∞性能,而并不要求每个子系统在整个状态空间上都满足鲁棒H∞性能,甚至也不要求其渐近稳定。
A class of state feedback robust H∞ control problems for switching systems consisting of any finite number of singular subsystems with parameter uncertainties and state delays is investigated. By using Lyapunov function method and convex combination technique, sufficient conditions for the existence of controllers represented by matrix inequalities are given and corresponding sub-controllers and switching rules are designed. Using a variable substitution method, the matrix inequality is transformed into a set of linear matrix inequalities (LMIs). Finally, a simulation example of the gain matrix of the state feedback controller in power system is given to prove the validity of the conclusion. The results show that, by switching, the closed-loop system satisfies robust H∞ performance at every point in the entire state space, and does not require that each subsystem satisfy the robust H∞ performance in the entire state space, nor even require It is asymptotically stable.