Control synthesis for enlarging the robust domain of attraction in uncertain polynomial systems

Abstract

This paper addresses the problem of control synthesis for enlarging the robust domain of attraction of equilibrium points in uncertain polynomial systems. Specifically, the system is described by polynomial functions of the state, whose coefficients are polynomially dependent on an uncertain vector constrained in a given set. The problem consists of designing a polynomial output controller that enlarges the domain of attraction of the equilibrium point of interest for all admissible uncertainties. For this problem we propose a strategy based on linear matrix inequality (LMI) optimizations and the square matrix representation (SMR) of polynomials. In particular, we show how the controller providing the largest estimate of the robust domain of attraction for a chosen parameter-dependent polynomial Lyapunov function can be computed by solving a quasi-convex optimization problem. A numerical example illustrates the use of the proposed strategy.