Constrained time-delay polynomial systems: A SOS-based stabilization approach to enlarge the domain of attraction

The problem of estimating the domain of attraction (DoA) of nonlinear time-delay polynomial systems subject to actuator saturation is considered in this paper via a Sum-of-Squares (SOS) approach. It will be shown that the joint use of sum-of-squares decomposition techniques and semidefinite programming provides an efficient methodology for the analysis and synthesis of polynomial nonlinear systems via Lyapunov stability arguments. Specifically, we present a two-step algorithmic procedure: first, a Lyapunov-Krasovskii functional/controller pair complying with the prescribed constraints is derived and then an estimate of the true DoA is determined. The effectiveness of the proposed framework is illustrated via a numerical example.