时变时滞不确定奇异摄动系统的保性能控制

为了保持鲁棒稳定且满足一定的性能指标要求, 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, 进行保性能控制分析。利用Lyapunov 稳定性理论及矩阵分析方法, 设计系统二次性能指标, 构造了Lyapunov-Krasovskii 泛函, 给出了系统鲁棒稳定的充分条件求解定理以及状态反馈保性能控制律, 得到了性能指标最小上界, 均用线性矩阵不等式形式给出。数值样例表明, 该方法对所研究系统保性能控制有效, 可推广到多状态滞后以及时变滞后的不确定系统的保性能控制问题。

Guaranteed Cost Control for Singularly Perturbed Uncertainty Control Systems with Time-Varying Time-Delay

In order to maintain robust stability while meeting certain performance index requirements, the problem of guaranteed cost control for time-varyiong time delay singularly perturbed systems with norm bounded uncertainty parameters is discussed. Using Lyapunov stability theory and matrix analysis method, based on a new quadratic L-Y performance index, the sufficient quadratic stability conditions, state feedback guaranteed cost control rate and the guaranteed cost index is presented by showed LMIs, and the minimum performance indication upper bound is derived. The method of the dissertation can be extended to multi-state delay uncertain systems guaranteed cost control problems, the numerical examples are employed to elaborate that this method is effective.