时变时滞奇异摄动系统的稳定性研究

Stability Analysis for Singularly Perturbed Systems with Time-varying Delay

针对时变时滞奇异摄动系统,该文用线性矩阵不等式方法给出了判定该系统稳定的充分条件。首先将此系统转化为一个与之等价的广义系统,然后基于线性矩阵不等式(LMI)方法,得到了该系统稳定且依赖于摄动参数的充分条件,为了消除由此带来的数值病态问题,该文将上述条件转化为与摄动参数无关的LMI条件。在此基础上,给出变时滞奇异摄动系统状态反馈控制器存在的充分条件,并由此得到了控制器增益。最后通过数值算例表明了上述方法的有效性。

Linear matrix inequalities （LMI） approach is used to make sure the sufficient condition for the stability of the singularly perturbed systems with time-varying delay. The system is transformed to an equivalent descriptor system. Based on a linear matrix inequalities approach, a sufficient condition for stability of the system is given. In order to eliminate the ill-conditioned numerical problems resulting from the perturbation parameter, the perturbation parameter dependent LMI condition is transformed into perturbation parameter independent one. The sufficient condition for the existence of the state feedback controller is given to guarantee the stability of the original system, and the controller gain is obtained. Some numerical examples are given to illustrate the efficiency of the approach.