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

Mai Thi Hong and Le Van Hien*
International Journal of Control, Automation, and Systems, vol. 19, no. 11, pp.3569-3579, 2021

Abstract : In this paper, the problem of L1-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 L1-stability and a new alternative approach using Laplace transformation is proposed to establish a characterization for L1-induced norm of the input-output operator. The obtained L1-induced norm characterization is then utilized to formulate necessary and sufficient conditions subject to L1-induced performance with prescribed level. Finally, based on some vertex optimization techniques, a complete solution to the stabilization problem under L1-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.

Keyword : Feasibility, linear programming, L1-gain control, positive systems.

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