A descriptor system approach to robust quadratic stability and stabilization of nonlinear systems

The problems of quadratic stability and stabilization for continuous-time systems subject to nonlinear perturbations are considered in this paper. By using a descriptor model transformation of the system, some less conservative conditions are given in terms of linear matrix inequalities. An optimization procedure is given to stabilize the systems and at the same time, maximize the bounds on the nonlinearities. Some numerical examples are presented to show the effectiveness of our method.