An LMI approach to persistent bounded disturbance rejection for a class of nonlinear impulsive systems

The problem of persistent bounded disturbance rejection for a class of nonlinear (Lipschitz-like) impulsive systems is considered through invariant set analysis using the Lyapunov function method. Conditions on a robust attractor for this class of systems are given in terms of linear matrix inequalities (LMIs), which ensure simultaneously internal stability and desired L1-performance. The obtained results are only dependent on the Lipschitz-like constant matrices without regard to the nonlinear forms. Based on the results, a simple approach to the design of a robust controller is presented. Finally, a numerical example is worked out to illustrate the efficiency of the theoretical results.