Synthesis of dynamic output feedback guaranteed cost controllers for a class of uncertain nonlinear systems

This paper deals with a design problem of a dynamic output feedback guaranteed cost controller for a class of uncertain nonlinear systems. The system considered here is composed of a linear part perturbed by an additive nonlinearity which depends on both time and state. Besides, only information about nonlinearity is that it satisfies a quadratic constraint. Our goal is to show an LMI-based design method of dynamic output feedback guaranteed cost controllers, and at the same time maximize the bounds on the nonlinearity which the system can tolerate without going unstable. In this paper, we show that sufficient conditions for the existence of the dynamic output feedback guaranteed cost controller are given in terms of LMIs. Finally, a numerical example is included.