Stability and stabilization for quadratic systems with state saturation nonlinearities

Abstract

This paper develops stability and stabilization results for a class of quadratic systems with state saturation nonlinearities. Based on the introduction of a row diagonally dominant matrix with negative diagonal elements and a particular representation for quadratic terms, sufficient conditions for stability and stabilization of quadratic systems with state saturation nonlinearities are derived in terms of a “quasi”-linear matrix inequality (LMI) form. Iterative LMI algorithms then are presented for checking global asymptotic stability and stabilization of the system. Numerical examples are provided to demonstrate the effectiveness of the proposed approach.