针对一类具有饱和执行器的不确定脉冲系统，研究了鲁棒线性反馈镇定及其吸引域估计问题。首先，对给定的状态反馈控制律，引入与脉冲时间序列关联的Lyapunov函数，并结合饱和函数的凸包表示，给出了零解鲁棒指数稳定性以及零解吸引域与脉冲区间长度的关系。然后，引入凸参考集，基于线性矩阵不等式，将求解使系统可鲁棒镇定的最大吸引域估计问题转化为凸优化问题。在脉冲区间上界信息已知的情形，本文结果改进了现有的结果。数值例子验证了本文方法的有效性和优越性。%Although many effective methods for robust control of uncertain dynamical systems with saturating actuators have been reported in the literatures , there are only a few results having taken into account of the effect of impulses on controller design and estimation of domain of attraction . The impulse disturbances degrade the system performance and increase the difficulties of system analysis . Therefore , it is of great importance to study the robust control problem of uncertain systems with input saturation under impulse disturbances . T he purpose of this paper is to investigate the problems of robust linear feedback stabilization and estimation of domain of attraction for a class of uncertain impulsive systems with saturating actuator . First , for a prescribed state feedback control law , by introducing a Lyapunov function associated with the impulse time sequence and by using the convex hull based representation of the saturation function , the relationship between the length of impulsive intervals and robust exponential stability and domain of attraction is built . T hen , by introducing the convex reference sets and by using the techniques of linear matrix inequalities , the problem of finding the largest estimation of domain of attraction such that the system can be robustly stable is transferred to a convex optimization problem . In the case that the knowledge of upper bound of impulsive intervals is known , the proposed results improve the existing ones . A numerical example is presented to show the validity and superiority of the derived results .
展开▼
