含状态时滞及执行器饱和不确定系统反馈镇定及L_2增益分析

Feedback stabilization and L_2-gain analysis of uncertain systems with state delay and actuator saturation

研究了具有控制饱和状态时滞不确定系统的L2控制问题,提出了状态反馈方法,利用Lyapunov函数可获得时滞相关的线性矩阵不等式.线性矩阵不等式条件可保证闭环系统无干扰时鲁棒内稳定性和在某椭球内预先给定的有干扰时L2性能水平,该不等式通过引入辅助矩阵解除了执行器饱和对系统的影响而更易于实现且减小了保守性.采用线性矩阵不等式技术,将控制器存在的充分条件转化为凸优化问题.在此基础上设计了系统的状态反馈控制器,最后用数值仿真验证了所提出方法的可行性.

The problem of L2 control for uncertain time-delay linear systems subject to actuator saturation is investigated in this paper. Firstly, the state feedback method is proposed and delay-dependent linear matrix inequality is achieved by Lyapunov function which ensures robust stability and a prescribed L2 performance level for the resulting closed-loop system in a given ellipsoid. An auxiliary matrix is then introduced that eliminates the effect of actuator saturation which enables us to obtain a more easily tractable and less conservative condition. Furthermore, sufficient conditions for the existence of state feedback controller are established in terms of linear matrix inequalities, in which the design of admissible controller is treated as a convex optimization problem. Finally, numerical example is provided to demonstrate the feasibility of the proposed method.