线性不确定时滞系统鲁棒指数镇定

Robust exponential stabilization for linearly uncertain time-delay systems

针对带有状态时滞的不确定线性时滞系统,基于Lyapunov稳定性理论,利用线性矩阵不等式方法讨论了系统鲁棒指数镇定的问题,提出了相应的无记忆状态反馈控制器设计方案。以线性矩阵不等式的形式给出控制器存在的充分条件,其中时滞参数为时变未知有界的,参数不确定性为时变未知满足匹配条件。所得结论与时滞参数及其导数均无关,克服了通常所得结论与时滞导数有关且要求时滞参数的导数小于某个小于1的常数的限制。应用实例证明了设计方案切实可行。

The Lyapunov stability theorem is used to analyze robust exponential stabilization problems in linear time-varying uncertain time-delay systems with state time-delays using the linear matrix inequality approach. The time-delay parameter is assumed to be a time-varying unknown but bounded. Sufficient conditions are given for the robust exponentially stabilization via linear matrix inequalities. A design strategy is then given for memoryless state feedback control. The results are independent of the scale of the time-delay and its derivative; where as most existing results are dependent on the time-delay derivative which must be less than a constant which is less than 1. An example is presented to illustrate application of the method.