离散时间切换双时标系统的建模与状态反馈控制

摘要

针对一类参数不确定性的线性离散时间双时标系统，将奇异摄动理论和切换理论相结合，建立离散时间切换双时标系统（DSTTSs）动态模型，切换理论的引入主要解决系统中参数不确定性部分对系统模型精确度的影响。主要讨论了离散时间双时标切换系统的稳定性分析以及状态反馈控制器的设计问题。利用谱范数法和线性矩阵不等式（LMIs）方法，将上述一系列问题都将归结为求解与摄动参数ε无关的线性矩阵不等式，并采用实例仿真证明该方法的有效性。%ABSTRACT:For a class of discrete-time singularly perturbed complex system with uncertain part, combining the singular perturbation theory with the switching theory, a dynamic model of switched discrete-time singularly perturbed systemsis builted. Switching mechanism is introduced to handle the unknown parameters, to achieve the precise control performance of the system. Stability a analysis and state-feedbackcontrol problems for switched discrete-time singularly perturbed systems (DSTTSs) are mainly investigated in this paper. With the spectral matrix normand linear matrix inequalities (LMIs) approaches , a series prob-lems are solved by a set ofε-independent linear matrix inequalities.A numerical example is presented to illustrate the effective-ness of the proposed approach.