An LMI approach to persistent bounded disturbance rejection for uncertain impulsive systems

The problem of persistent bounded disturbance rejection for linear impulsive systems with parametric uncertainty is considered by Lyapunov function and positively invariant set analysis method. A sufficient condition for robustly internal stability and L₁-performance of the impulsive systems is obtained in terms of linear matrix inequalities. Based on this result, a simple approach to the design of a linear state-feedback controller is presented to stabilize robustly the uncertain impulsive systems and achieve a desired level of disturbance attenuation. A numerical example is given to illustrate the efficiency of the proposed approach.