Robust quadratic stabilization for a class of discrete-time nonlinear uncertain systems: A genetic algorithm approach

We present in this paper a new approach, to check the stability robustness of discrete-time systems under nonlinear perturbations. The systems are composed of a linear constant part perturbed by an additive nonlinearity. The unique information about the nonlinearity is that it satisfies a quadratic constraint. Our objective is to design a state feedback control law that maximizes the bound on the nonlinearity which the system can tolerate without destroying its stability. All results are obtained within the framework of a Genetic Algorithm (GA). The effectiveness of the method is illustrated through an example.