L1 ‐gain control on positive impulsive system via a hybrid proportional plus integral algorithm

• Published in: IET control theory & applications Vol. 13; no. 7; pp. 898 - 904
• Main Authors: Chen, Hao, Zhan, Tao, Huang, Qinzhen
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 30.04.2019
• Subjects: control system synthesis; convex programming; co‐positive Lyapunov function method; gain control; hybrid proportional plus integral algorithm; impulse instants; impulse time intervals; impulse‐time‐dependent control algorithm; impulsive interval approach; impulsive positive system; integral control scheme; integral control strategy 𝒦1; iterative convex optimisation algorithm; iterative methods; linear programming; linear programming problem; Lyapunov methods; matrix algebra; PII control gain matrices; positive impulsive system; proportional control action Kp; stability; time‐varying systems; ℒ1 ‐gain control issues
• ISSN: 1751-8644; 1751-8652
• DOI: 10.1049/iet-cta.2018.5251

In this study, the L1 ‐gain control issues on positive system are investigated. A hybrid proportional impulsive with integral (PII) control scheme is proposed. This impulse‐time‐dependent control algorithm uses the proportional control action Kp at impulse instants for stabilising, and applies the integral control strategy KI between impulse time intervals for improving the state convergence, respectively. The average impulsive interval approach and co‐positive Lyapunov function method are employed to derive the sufficient conditions. Then L1 ‐gain performance of the impulsive positive system can be guaranteed by solving the linear programming problem. In addition, iterative convex optimisation algorithm is presented for the design of PII control gain matrices. Numerical examples illustrate the expected results of this design.