离散广义系统的H_2与H_∞控制

H_2 and H_∞ controls of discrete singular systems

利用矩阵不等式的方法和广义Liapunov函数,首先研究了离散广义系统的H∞状态反馈控制问题,得出判定一类离散广义系统的正则、因果、稳定性问题和H∞范数有界的一个充分必要条件,同时给出一个容许的闭环系统状态反馈控制器.其次,研究了一类不确定离散广义系统的H2性能指标问题,当容许的不确定参数范数有界时,得出判定不确定离散广义系统正则、因果、稳定且满足H2性能指标的充分条件.

By using matrix inequality method and singular Liapunov function, H∞ state feedback control problem for a discrete singular system is studied. A necessary and sufficient condition for the system to be regular, and satisfy a prescribed H∞-nom condition is obtained and a admissible state feedback controller is given. The second, the H2 performance criterion for a class of uncertain discrete singular systems are discussed, the admissible uncertainty are norm-bounded. A sufficient condition for an uncertain discrete singular system to be regular, causal, stable and possess H2 performance criterion is given.