时滞离散系统的鲁棒稳定新判据及控制器设计

针对一类具有多重状态时滞和多面体不确定性的离散时间系统,提出了一个新的参数依赖型 Lya-punov 稳定条件,并基于此条件设计了系统的鲁棒镇定状态反馈控制器。采用线性矩阵不等式(LMI)技术,将控制器存在的充分条件转化为 LMI 的解存在条件,可以采用较为有效的内点方法进行求解.与已有的基于二次稳定的结果相比,表明所提出的方法具有较低的保守性,通过数值仿真验证了所提出算法的可行性和优越性.

New robust stability condition and controller design for uncertain time-delayed discrete-time systems

The problem of robust stabilization is solved for discrete-time uncertain systems with multiple state delays the uncertain parameters are supposed to belong to a given convex bounded polyhedral domain.The aim is to design a stable linear state feedback controller assuring asymptotic stability irrespective of the uncertain- ties and the time delays.A new robust parameter-dependent stability condition is proposed and corresponding controller design is presented in terms of linear matrix inequalities(LMI),which can be efficiently solved by the so called interior point algorithms.Compared with earlier results based on quadratic stability notion,the method proposed in this paper is less conservative,which is illustrated by numerical examples at the end of the paper.