基于增广Lyapunov泛函的时滞系统鲁棒H_∞控制

研究了一类时滞系统的鲁棒H∞控制问题.利用增广Lyapunov泛函并结合自由权矩阵方法,以严格线性矩阵不等式(LMIs)的形式给出了保证闭环系统渐近稳定且具有给定H∞性能的改进的时滞相关有界实引理(BRL).基于得到的BRL,以LMIs的可行解给出了记忆型的状态反馈H∞控制律.当时滞系统存在范数有界不确定性时,同样地给出了基于LMIs的记忆型鲁棒H∞控制律的具体设计方法.仿真实例表明了该方法的有效性以及更小保守性.

Robust H∞ Control for Time-Delay Systems Based on Augmented Lyapunov Functionals

The problem of delay-dependent robust H∞ control for systems with state-delay was investigated.An improved delay-dependent bounded real lemma(BRL) was established in terms of linear matrix inequalities(LMIs) by using augmented Lyapunov functionals and free-weighting matrices method,ensuring the resultant closed-loop system asymptotically stable and a prescribed H∞ performance level.Based on the obtained BRL,the state feedback H∞ control law with memory was given in terms of the feasible solutions of LMIs.When the time-varying norm-bounded uncertainties appeared in a time-delay system,the explicit design approach of the robust H∞ controller was also given and formulated in the form of LMIs.Numerical examples are provided to demonstrate the reduced conservatism and validity of the proposed conditions.