状态饱和离散线性系统的稳定性分析

Stability analysis for discrete-time linear systems with state saturation

讨论一类具有状态饱和非线性的离散线性系统稳定性分析问题.通过引入无穷范数小于等于1的自由矩阵与对角元素非正的对角矩阵,将状态饱和离散线性系统的状态变量约束在一个凸多面体内,进而以矩阵不等式形式给出状态饱和离散线性系统的稳定性判据,并给出该矩阵不等式的迭代线性矩阵不等式算法.基于这一稳定性判据,给出了基于迭代线性矩阵不等式的状态反馈控制律设计算法.通过状态饱和离散线性系统的状态空间分割方法,给出了保守性更小的稳定性判据,并给出了相应的迭代线性矩阵不等式算法.数值例子验证了所给出方法的正确性与有效性.

The stability analysis for a class of discrete-time linear systems with state saturation nonlinearity is concemed.By introducing a free matrix with infinity norm less than or equal to 1 and a diagonal matrix with nonpositive diagonal elements, the state of this discrete-time linear system under state saturation constraint is confined in a convex hull. In this way, a criterion for discrete-time linear systems with state saturation to be asymptotically stable is obtained in terms of bilinear matrix inequalities that can be resolved by using the presented iterative linear matrix inequality algorithm. Based on this criterion, the state feedback control law synthesis problem is also resolved and the corresponding iterative linear matrix inequality algorithm is given. A further study shows that the space division method can be also applied to solve this problem with less conservativeness. Numerical examples are used to illustrate the effectiveness and correctness of the proposed method.