参数不确定广义时滞系统的保性能控制

Guaranteed cost control for singular systems with time-delay and parameter uncertainty

针对状态时滞的参数不确定性广义系统,讨论了它的保性能控制问题。目的是对状态时滞的参数不确定广义系统,提出它的时滞无关保性能鲁棒控制器的一个设计方法。首先给出了广义时滞系统正则、脉冲自由且稳定的严格线性矩阵不等式表示的时滞无关充分条件;然后采用线性矩阵不等式方法,给出参数不确定性广义时滞系统的时滞无关保性能控制问题可解的一个严格线性矩阵不等式表示的充分条件,在此条件可解时,给出了时滞无关保性能鲁棒控制器表达式,以及相应的可保性能指标。最后给出了所提出方法的应用。

The guaranteed cost control problem is studied for singular systems with time-delay and parameter uncertainty. The aim is to design a delay-independent guaranteed cost controller for singular systems with time-delay and parameter uncertainty. First, a delay independent sufficient condition which is xepressed by strict linear matrix inequality （LMI）, for the singular systems with time-delay to be regular, impulse free and stable is derived. The delayindependent sufficient condition for the existence of guaranteed cost controller is given in terms of strict linear matrix inequalities via LMI approach. When these LMIs are feasible, an explicit expression of delay-independent robust guaranteed cost controllers and the corresponding guaranteed cost of the systems are obtained. Finally, a numerical example is provided to demonstrate the application of the proposed method.