Domain of attraction and guaranteed cost control for non-linear quadratic systems. Part 1. Analysis

This is the first study of a two-part work devoted to the stability analysis and guaranteed cost control of the class of non-linear quadratic systems. For a given polytopic region in the state space, a sufficient condition is proposed to check whether an assigned region belongs to the domain of attraction of the zero equilibrium point. It is also shown that this problem is intimately related to the convergence and the computation of quadratic cost functions. Thanks to the main result of the study, both issues are casted in terms of feasibility problems involving linear matrix inequalities. A meaningful application example, involving the development of optimal strategies for integrated pest management, is illustrated at the end of this study.