An LMI approach to persistent bounded disturbance rejection for impulsive systems with polytopic uncertainties

The problem of persistent bounded disturbance rejection for uncertain linear impulsive systems is considered in this paper. The systems under consideration is subject to polytopic uncertainties appearing in all matrices of the state-space model. By using positive invariant set and Lyapunov function methods, a sufficient condition for robust internal stability and L ₁-performance of the impulsive systems is established 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 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 uncertainties. A numerical example is worked out to illustrate the efficiency of the proposed approach and less conservatism of the newly obtained results.