Quadratic Stability and Quadratic Stabilizability for Singularly Perturbed System

Quadratic stability is proposed for singularly pert urbed continuous systems. Using the linear matrix inequality, a sufficient condition is derived for quadratic stability and another sufficient condition is given for quadratic stabilizability and solvability of singularly perturbed systems. A feedback controller for quadratic stabilization is designed with an iterative algorithm. An example is worked out to illustrate the effectiveness of the method and the simulation results are given by the MATLAB tool box. The method is effective for stiff questions by comparing with that of regular systems.