带有控制器时滞的不确定奇异离散系统鲁棒保代价控制

Robust guaranteed cost control for uncertain singular discrete systems with time-delay in controller

针对一类具有范数有界时变参数不确定性的奇异离散系统和二次型代价指标,研究了奇异系统的鲁棒保代价控制律的设计问题。在所设计的控制器中,考虑了时滞因素。通过构造Lyapunov函数,以矩阵不等式的形式,导出了存在保代价控制律的充分条件,并利用Schur补性质,将该矩阵不等式转化为线性矩阵不等式的可解性问题,通过求解线性矩阵不等式,就可得到奇异离散系统的鲁棒保代价控制器。最后,用一个数值例子验证了所给方法的可行性、有效性。

For a class of singular discrete systems with norm-bounded time-varying parameter uncertainty and a quadratic cost function,the robust guaranteed cost control is studied.Time-delay is also considered in the controller design.Based on Lyapunov stability theory,a sufficient condition for the existence of robust guaranteed cost controllers is derived.By using Schur complement,it is shown that this condition is a solvable problem of linear matrix inequalities（LMI）,and its solutions provide a parameterized representation of robust guaranteed cost controllers.At last,a numerical example is presented to illustrate the feasibility and validity of this approach.