Stability analysis and controller synthesis for non-linear quadratic systems with time delay

This paper is devoted to stability analysis and controller synthesis for non-liner quadratic systems with time delay. In the (local) stability analysis problem, the objective is the determination of estimates of the Domain of attraction of the system, considering the stabilization and controller synthesis problems, the goal is to design a set of gains in order to enlarge the Domain of attraction of the closed-loop systems as large as possible. Based on the quadratic Lyapunov functions, Razumikhin-type techniques and a particular presentation for the quadratic systems, delay in-dependent stability conditions are derived in terms of “quasi” linear matrix inequalities. From these conditions, convex optimization strategies are presented to solve both problems. Some examples are given to verify the effectiveness of the methodology proposed in this study.