Premium
Finite‐time ℒ 1 control via hybrid state feedback for uncertain positive systems with impulses
Author(s) -
Hu MengJie,
Park Ju H.
Publication year - 2020
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.5365
Subject(s) - control theory (sociology) , interval (graph theory) , controller (irrigation) , state (computer science) , lyapunov function , mathematics , control (management) , full state feedback , upper and lower bounds , computer science , nonlinear system , algorithm , mathematical analysis , physics , combinatorics , artificial intelligence , quantum mechanics , agronomy , biology
In this study, the finite‐timeℒ 1control 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‐timeℒ 1characterization 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 allowableℒ 1‐gain level are revealed. Numerical examples are used to illustrate the usefulness of the theoretical results.