时滞独立状态下离散控制系统的稳定性分析  

Stability analysis for discrete control system in delay-independent state

作　　者：孙凤琪[1] SUN Feng-qi(School of Mathematics,Jilin Normal University,Siping 136000,China)

机构地区：[1]吉林师范大学数学学院,吉林四平136000

出　　处：《东北师大学报（自然科学版）》2021年第3期36-39,共4页Journal of Northeast Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(61741318).

摘　　要：针对一类系统矩阵中含有不确定性、系统状态中含有时变时滞的时滞奇异摄动不确定性综合控制系统,进行了时滞独立的稳定性分析.通过构造一种含有奇异摄动的双二次型Lyapunov泛函,推出系统渐近稳定性判据,给出鲁棒稳定区间以及奇异摄动的最小上界,继而给出相应推论.最后用数值样例说明所得方法的有效性和可行性,并展示了时滞独立情形下的鲁棒稳定性所具有的理论价值和优越性.Based on Lyapunov stability theory,matrix analysis methods and cross item defined method,the delay-independent stability analysis is discussed for a class of singularly perturbed uncertain integrated control system with time-varying delays and uncertainties in the system state vector and system matrix,By constructing a biquadratic Lyapunov functional with singular perturbation,the asymptotic stability criterion of the system is derived,the robust stability interval and the minimum upper bound of the singular perturbation are given,then,the corresponding inference is given.Finally,the feasibility and superiority are illustrated by the selected numerical example in terms of the proposed method,and to demonstrate the theoretical value and advantages of robust stability in the case of time delay independence.

关 键 词：不确定性 线性矩阵不等式 时滞独立 LYAPUNOV泛函 时滞分段分析方法 

分 类 号：O231.2[理学—运筹学与控制论]