Saturated impulsive control of nonlinear systems using Sum of Squares approach

In this article, the stability and stabilization problems of saturated impulsive nonlinear control systems are investigated. With the use of a class of clock-dependent Lyapunov functions and polytopic representation approach, new sufficient conditions ensuring the local exponential stability (LES) are established in the framework of dwell time, which allow that both the continuous and discrete parts of the systems are destabilizing at the same time. Moreover, based on the sum of squares programming, an optimization algorithm is proposed to design the saturated impulsive controller with improvement of the allowable impulsive dwell-time and the size of the domain of attraction. Finally, the simulation results demonstrate the effectiveness of the results.