Persistent bounded disturbance rejection for impulsive systems with polytopic uncertainties

The problem of bounded disturbance rejection for linear impulsive systems with polytopic uncertainties is considered in this paper. By using the Lyapunov function and positively invariant set method, a sufficient condition for robustly internal stability and L1-performance of the impulsive systems is obtained in terms of linear matrix inequalities. A simple algebraic approach to the design of a linear state-feedback controller that robustly stabilizes the system and achieves a desired level of disturbance attenuation is proposed. Furthermore, since the Lyapunov function matrix is decoupled from coefficient matrices in the newly obtained sufficient criterion, it is convenient to study the robustness problem for impulsive systems with respect to polytopic uncertainty. A numerical example is worked out to illustrate the efficiency of the proposed approach and less conservatism of the newly obtained results.