Exponential Stability With $L_{2}$ -Gain Condition of Nonlinear Impulsive Switched Systems

In this technical note, we consider exponential stability and stabilization problems of a general class of nonlinear impulsive switched systems with time-varying disturbances. By using the switched Lyapunov function method, sufficient conditions expressed as algebraic inequality constraints and linear matrix inequalities are obtained. They ensure that the nonlinear impulsive switched systems are not only exponentially stable but also satisfy the L₂-gain condition. Based on the stability results obtained, an effective computational method is devised for the construction of switched linear stabilizing feedback controllers. A numerical example is presented to illustrate the effectiveness of the results obtained.