Robust stabilization approach and H ∞ performance via static output feedback for a class of nonlinear systems

Abstract

This paper deals with the stability and stabilization problems for a class of discrete-time nonlinear systems. The systems are composed of a linear constant part perturbated by an additive nonlinear function which satisfies a quadratic constraint. A new approach to design a static output feedback controller is proposed. A sufficient condition, formulated as an LMI optimization convex problem, is developed. In fact, the approach is based on a family of LMI parameterized by a scalar, offering an additional degree of freedom. The problem of performance taking into account an H ∞ criterion is also investigated. Numerical examples are provided to illustrate the effectiveness of the proposed conditions. © 2009 Neila Bedioui et al.