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讨论不确定广义系统时滞相关的鲁棒同时H_∞控制问题。首先,通过引入Lyqpunov-Krasovskii泛函以线性矩阵不等式(LMI)形式给出时滞相关的新有界实引理,使得系统正则、无脉冲、稳定且具有H_∞性能。其次,在有界实引理基础上得到广义闭环系统的同时H_∞控制器存在的时滞相关的充分条件。进一步推广到不确定广义时滞闭环系统中,并给出鲁棒同时H_∞控制器的的设计方法。控制器可由一组线性矩阵不等式(LMI)求解得到,避免了系统中矩阵的分解。最后,由仿真算例说明该设计方法的有效性。
The problem of robust simultaneous H_∞ control for uncertain singular systems is discussed. First, a new bounded real lemma with delays is given by introducing Lyqpunov-Krasovskii functional in the form of linear matrix inequality (LMI), which makes the system regular, pulse-free, stable and H_∞ -like. Secondly, the sufficient conditions for the existence of delay-dependent perturbations for the generalized closed-loop systems are obtained on the basis of bounded real lemmas. It is further extended to the uncertain generalized closed-loop system with time-delay and the design method of robust simultaneous H_∞controller is given. The controller can be solved by a set of linear matrix inequalities (LMIs) to avoid the decomposition of the matrix in the system. Finally, a simulation example shows the effectiveness of the design method.