Application of Sum-of-Squares Method in Estimation of Region of Attraction for Nonlinear Polynomial Systems

We present a sum of squares (SOS) method for the synthesis of nonlinear polynomial control systems. As an emerging numerical solution method in recent years, SOS targets polynomials as the research object. It guarantees that the polynomial we solve for is always nonnegative. In this paper, we give a generalized S-procedure to solve the SOS problem. As an illustration of how the SOS method can be used, the region of attraction (ROA) in a nonlinear polynomial system is analyzed in detail. The method of determining decision variables is given in the SOS problem. We discuss the determination and solution of set-containment constraints and the conservatism problem in solving the SOS problem. SOS provides a convenient numerical method to solve nonlinear problems that are not easy to solve analytically.