时滞奇异摄动控制系统的稳定性分析

为保持系统的稳定性, 针对具有范数有界不确定性参数的不确定时滞奇异摄动控制系统, 进行鲁棒稳定性分析。给出系统稳定性的补充定义, 并在此基础上构造Lyapunov-Krasovskii泛函, 提出了时滞依赖和时滞独立情况下的系统鲁棒稳定的充分条件和求解定理, 对所有结果均进行严格理论推导并以矩阵不等式形式
给出。由于该方法所选取的是更一般的Lyapunov-Krasovskii泛函, 与已有方法相比, 具有较小的保守性, 该Lyapunov-Krasovskii泛函可以用于研究其他时滞奇异摄动系统的分析和设计问题。

Stability Analysis for Singularly Perturbed Control System with Time-Delay

In order to maintain the stability of the system, the problem of robust stability analysis is investigated for uncertain time-delay singularly perturbed systems with norm bounded uncertainty parameters. Based on the supplement definition, for the case of delay-dependent and delay-independent, the sufficient robust stability judgment conditions and the corresponding existent theorem are deduced respectively by constructing the new Lyapunov-Krasovskii functionals. Compared with the existing literatures, the innovation that the resulting method in the form of matrix inequalities and strictly theoretical derivation is less conservative, because of the selected broader general Lyapunov-Krasovskii functionals. It can be used to study other delay perturbation system analysis and design issues.