Finite-time Script capital L1 control via hybrid state feedback for uncertain positive systems with impulses

In this study, the finite-time Script capital L1 control for uncertain positive systems with impulses using a hybrid state feedback control mechanism is investigated. The hybrid state feedback double control strategy is utilized, which includes impulsive state control scheme and continuous state feedback control scheme. A type of time-varying Lyapunov copositive function is constructed. Considering different impulsive effects, the finite-time boundedness criterion is obtained by applying the average impulsive interval approach. In addition, sufficient conditions are proposed for finite-time Script capital L1 characterization analysis and the hybrid state feedback controller design. All the criteria can be checked by the linear programming approach succinctly. The relationships among the upper bound of the finite-time interval, the frequency and intensity of impulses, and the minimum allowable Script capital L1-gain level are revealed. Numerical examples are used to illustrate the usefulness of the theoretical results.