一类切换时滞奇异系统的最优保成本控制

Optimal guaranteed cost control for a class of switched singular systems with time-delay

针对一类切换时滞奇异系统,对最优保成本控制问题进行了研究。利用Lyapunov函数方法和凸组合技术,给出了由线性矩阵不等式(linear matrix inequality,LMI)表示的保成本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。进一步,建立了一个具有线性矩阵不等式约束的凸优化问题,利用Matlab软件中的线性矩阵不等式工具箱求解,给出了最优保成本控制器的设计方法及闭环最小性能指标上界。仿真示例验证了该方法的有效性。

The problem of optimal guaranteed cost control for a class of switched singular systems with time-delay is considered.By means of Lyapunov function approaches and convex combination techniques,a sufficient condition for the existence of guaranteed cost sub-controllers is presented,which is in the form of linear matrix inequalities（LMIs）,accordingly,both sub-controllers and switching strategy are designed.Furthermore,a convex optimization problem with LMIs constraints is formulated,the design of optimal guaranteed cost sub-controllers and the minimization of the upper boundary of closed-loop performance index are obtained by using the LMI toolbox in Matlab.Finally,a numerical example shows that the obtained results are effective.