Guaranteed cost control of uncertain impulsive switched systems with nonlinear disturbances

This paper discusses a guaranteed cost control problem of an uncertain impulsive switched system with nonlinear disturbances. The contribution of this study is to extend guaranteed cost control from traditional systems to uncertain impulsive switched systems with nonlinear disturbances. Firstly, an uncertain impulsive switched system with nonlinear disturbances is stated and some important definitions are given. Secondly, the stability of the closed-loop uncertain impulsive switched system with a linear quadratic guaranteed cost control law is proved and the upper boundary of performance cost is discussed. Especially, different from traditional stability analysis of impulsive switched systems without disturbances, above conclusions are given under a nonlinear disturbance. Thirdly, Linear Matrix Inequality (LMI) formulation is utilized to design the optimal guaranteed cost control law of the uncertain impulsive switched system. Finally, simulations are carried on to demonstrate the proposed algorithm.