离散时间奇异摄动系统的H_∞控制

H∞ control of discrete-time singularly perturbed systems

研究了离散时间奇异摄动系统的H∞控制问题.基于线性矩阵不等式,给出了求奇异摄动参数ε上界的一种方法.得到了一个求容许上界ε*的充分条件,使得对于任意的ε∈(0,ε*],离散时间奇异系统是渐近稳定的并且满足给定的H∞范数约束.通过数值例子验证了方法的有效性.

The problem of H∞ control of discrete-time singularly perturbed systems is studied.A method of evaluating the upper bound of singular perturbation parameter ε is given in terms of linear matrix inequalities.A sufficient condition on searching for the allowable upper bound ε＊ is obtained,so that the discrete-time singularly perturbed system is asymptotically stable and satisfies a prescribed H∞ norm bound for any singular perturbation parameter ε∈（0,ε＊].A numerical example is given to illustrate the effectiveness of the proposed method.