离散时滞奇异摄动控制系统的稳定性分析

Stability Analysis of Discrete Time-Delay Singularly Perturbed Uncertainty Control Systems

对含不确定性结构的奇异摄动时滞离散控制系统进行稳定性研究.通过设计一种新的Lyapunov-Krasovskii泛函,基于Lyapunov稳定性理论,在时滞依赖情形下,采取交叉项界定技术、线性矩阵分析方法并运用引理,推出在零到奇异摄动上界的整个区间范围内系统渐近稳定,给出充分性的稳定性判据.之后,再对其进行理论加深和推广,得到更加简洁性的推论,可以借助于MATLAB工具箱进行求解.最后,用算例证明本文所得方法的优越性和可行性.

The stability of discrete control systems with time delay,singular perturbation and uncertainty was studied.With a designed new Lyapunov-Krasovskii functional,based on the cross term defined technique,the linear matrix analysis method and the related lemmas,and furthermore,according to the Lyapunov stability theory,the asymptotic stability of the system in the entire interval from zero to the singularly perturbed upper bound was derived in the time-delay-dependent case.Then the sufficient stability criterion was given,which was deepened and generalized to deduce the linearized inferences,and solved with the MATLAB toolbox.The example illustrates the superiority and feasibility of the obtained method.