不确定离散时间系统鲁棒稳定控制

ROBUST STABILIZING CONTROL FOR DISCRETE-TIME UNCERTAIN SYSTEMS

根据Ｌｙａｐｕｎｏｖ稳定性定理，针对不确定离散时间系统鲁棒稳定状态反馈控制问题，提出一种方法，即通过不确定矩阵秩１分解，计算加权矩阵，沿用线性最优调节器问题的Ｒｉｃｃａｔｉ代数方程，设计鲁棒稳定调节器，并讨论了控制矩阵的不确定程度与鲁棒稳定调节器的存在性关系问题。

Based on the Lyapunov stability criterion, in this paper we present a method to study the robust stabilizing feedback control law for uncertain discrete-time systems. This method can be used to calculating the weighted matrix in terms of the solution of a matrix whose uncertainty is of 'rank-1' type, and then designing the robust stabilizing controller according to the Riccati equation about the linear optimal controller. Meanwhile, we also discuss the uncertainly of the control matrix and the existence of robust stabilizing controller.