基于线性矩阵不等式的时滞广义系统的稳定性与镇定

Stability and Stabilization of Singular Systems with Time-Delay:an LMI Approach

研究了时滞广义系统的稳定与镇定问题。利用广义二次稳定和广义二次镇定的概念,应用线性矩阵不等式方法分别给出了时滞广义系统广义二次稳定和广义二次镇定的充要条件,它们都是一严格的线性矩阵不等式,同时给出了相应的控制器表达式。最后,举例说明了给出方法的应用。

The stability and stabilization problems are studied for singular systems with time-delay. These problems are solved via the notions of generalized quadratic stability and generalized quadratic stabilization. Necessary and sufficient conditions for generalized quadratic stability and generalized quadratic stabilization are derived via linear matrix inequality （LMI）. They are strict linear matrix inequalities （LMI）, respectively. An explicit expression for the desired generalized quadratic stabilization state feedback control law is also given. Finally, a numerical example is provided to demonstrate the application of the proposed method.