圆形区域极点约束下的δ算子时滞系统鲁棒L2-L∞控制

研究了δ算子线性参数不确定时滞系统具有圆形区域极点约束的鲁棒L2-L∞控制问题。根据矩阵理论,以矩阵不等式形式给出δ算子时滞系统极点位于圆形区域内的一个充分条件。针对受扰的δ算子线性参数不确定时滞系统,利用Lyapunov稳定性理论,提出满足圆形区域极点约束的最优鲁棒L2-L∞状态反馈控制器的设计方法,控制器可以确保对于所有的容许不确定性,δ算子闭环时滞系统的极点都位于稳定域内的指定圆形区域中,并使系统的鲁棒L2-L∞性能指标尽可能小。数值算例验证了设计方法的可行性和有效性。

Robust L2-L∞ control of δ operator formulated time-delay systems with disc regional pole constraint

The problem of robust L2-L∞ control with disc regional pole constraint was investigated for a class of δ operator formulated linear time-delay uncertain systems. Based on the matrix theory, a sufficient condition for the poles of a δ operator formulated linear time-delay system, being inside a disc region, was presented in the form of linear matrix inequality (LMI). For a class of δ operator time-delay uncertain systems with disturbances, a design method of the optimal robust L2-L∞ controller was obtained by the Lyapunov approach, which could place the poles of the closed loop system in a prespecified disc and ensure the L2-L∞ performance to be optimal, . A numerical example was provided to illustrate the feasibility and effectiveness of the design method.