Enlarging Domain of Attraction for a Special Class of Continuous-time Quadratic Lyapunov Function Piecewise Affine Systems based on Discontinuous Piecewise

This paper presents a new approach to estimate and to enlarge the domain of attraction for a planar continuous-time piecewise affine system. Various continuous Lyapunov functions have been proposed to estimate and to enlarge the system’s domain of attraction. In the proposed method with a new vision and with the aids of a discontinuous piecewise quadratic Lyapunov function, the domain of attraction at the origin is enlarged by designing a state feedback controller. This paper shows that the continuity of the Lyapunov function on the boundaries, increases the conservativeness in estimating the domain of attraction, and gives more powerful search ability to the domain of attraction estimation algorithm by relaxing this continuity condition. The simulation results show the superiority of the proposed method so that using this method the larger estimation of the domain of attraction is obtained than continuous one.