Lyapunov stability analysis and controller design for rational polynomial systems using sum of squares programming

摘要

In this paper, Lyapunov stability of systems with rational polynomial dynamics is investigated by using sum of squares (SOS) programming methods and polynomial Lya-punov functions. An optimization based algorithm is proposed in order to design a stabilizing controller which maximizes the region of attraction. As the decision variables are being multiplied together, and therefore, the optimization problem is bilinear, the iteration method based on bisection is used in order to gradually enlarge the region of attraction. The positive definiteness conditions are relaxed into SOS conditions. The proposed controller design and stability analysis algorithm is evaluated by simulating a bidirectional power converter feeding a constant power load (CPL).