Solvability of L1-induced Controller Synthesis for Positive Systems with Multiple Delays

• Published in: International journal of control, automation, and systems Vol. 19; no. 11; pp. 3569 - 3579
• Main Authors: Hong, Mai Thi, Van Hien, Le
• Format: Journal Article
• Language: English
• Published: Bucheon / Seoul Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers 01.11.2021; Springer Nature B.V; 제어·로봇·시스템학회
• Subjects: Algorithms; Control; Engineering; Linear programming; Linear systems; Mechatronics; Optimization; Optimization techniques; Regular Papers; Robotics; Stability; 제어계측공학; gain control; Feasibility; linear programming; positive systems
• ISSN: 1598-6446; 2005-4092
• DOI: 10.1007/s12555-020-0510-x

In this paper, the problem of L 1 -gain control is studied for a class of positive linear systems with diverse state and output delays. A necessary and sufficient stability condition is first quoted via the concepts of exponential stability and L 1 -stability and a new alternative approach using Laplace transformation is proposed to establish a characterization for L 1 -induced norm of the input-output operator. The obtained L 1 -induced norm characterization is then utilized to formulate necessary and sufficient conditions subject to L 1 -induced performance with prescribed level. Finally, based on some vertex optimization techniques, a complete solution to the stabilization problem under L 1 -gain control scheme is formulated through tractable linear programming conditions, which can be effectively solved by various convex algorithms. Numerical examples and simulations are given to illustrate the effectiveness of the proposed method in this paper.