不确定离散时滞系统的鲁棒H_∞控制

Robust H_∞ reliable control for uncertain discrete time-delay systems

针对一类含有离散时滞的不确定参数线性系统,研究了鲁棒H∞可靠控制器的设计问题。经过适当的状态变换,将原系统的鲁棒可靠镇定问题转化为另一个等价系统的鲁棒可靠镇定问题。根据Lyapunov稳定性理论,给出了系统存在稳定鲁棒可靠控制器应满足的一个矩阵不等式;同时给出了系统具有H∞性能指标应满足的另一个矩阵不等式。将这一个矩阵不等式转化为一个线性矩阵不等式(LMIs)。鲁棒H∞可靠控制器能够使得时滞系统对于任意允许的不确定性都保持鲁棒可靠稳定,并且使系统具有指定H∞范数的抗干扰抑制能力。

The problem of robust H∞ reliable control for time-varying delayed uncertain discrete systems is researched. By means of model transformation, the robust reliable stabilization problem is reduced to an equivalent robust reliable stabilization problem. Based on Lyapunov stability theory, a sufficient condition of the existing of robust reliable controller with stability is given. At the same time, another sufficient condition of the existing of robust reliable controller possessing H∞ performance index is presenied. Those conditions are transformed to one linear matrix inequalities （LMIs）. The resulting control systems retain robust reliable stability and disturbance attenuation with H∞-norm bounds.