The central point of this paper is the problem of robust stability and robust control design for a class of continuous-time singularly perturbed systems with time varying norm bounded uncertainties in all systems matrices. By using the fixed point principle, a sufficient condition to guarantee that the given system is in the standard from is given. Secondly the two time scale technique is applied to decompose the system into slow and fast subsystems. Based on the slow and fast subsystems, the problem of robust uncertainty alleviation with stability and control is solved via the notion of generalized quadratic stability and stabilization with norm bound for all sufficiently small values of the perturbation parameter. Necessary and sufficient conditions for generalized quadratic stability and stabilizability with a prescribed performance level are derived. Our result which has not been discussed in earlier reports can be regarded as extensions of existing results on control and robust stabilization.

Index Terms- SingularlyPerturbed Systems (SPSs), Linear Matrix Inequality (LMI), Generalized Quadratic Stability (GQS), Robust Analysis and Control