Stability Analysis for Singularly Perturbed Systems with Time-varying Delay

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.