Persistent bounded disturbance rejection for impulsive systems with parametric uncertainties: An LMI approach

The problem of persistent bounded disturbance rejection for linear impulsive systems with parametric uncertainties is considered by Lyapunov function and positively invariant set analysis method. A sufficient condition on robust internal stability and L₁-performance of the impulsive systems is established in terms of linear matrix inequalities. Based on this result, a simple approach to design a linear state-feedback controller is presented to stabilize robustly the impulsive systems with uncertainties and to achieve a desired level of disturbance attenuation. A sufficient condition on the existence of a non-fragile state-feedback controller is also obtained. Two numerical examples are worked out to illustrate the feasibility and efficiency of the proposed approach.