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

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  • Control Theory and Applications
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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.

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Authors and Affiliations

  1. Department of Mathematics, National University of Civil Engineering, 55 Giai Phong, Hanoi, Vietnam

    Mai Thi Hong

  2. Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy, Hanoi, Vietnam

    Le Van Hien

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  1. Mai Thi Hong
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  2. Le Van Hien
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Correspondence to Le Van Hien.

Additional information

Recommended by Associate Editor Shun-ichi Azuma under the direction of Editor Yoshito Ohta

This research is funded by National University of Civil Engineering (NUCE) under grant number 14-2020/KHXD-TD.

Mai Thi Hong received her B.Sc. and M.Sc. degrees in mathematics from Hanoi National University of Education and Hanoi Institute of Mathematics, Vietnam Academy of Science and Technology, in 1998 and 2002, respectively. Ms. Hong began with National University of Civil Engineering in 1998, where she is currently a lecturer in mathematics. She is pursuing a Ph.D. degree in mathematics with Hanoi National University of Education. Her research interests include the system and control theory for complex dynamical systems including positive systems and time-delay systems.

Le Van Hien received his B.Sc., M.Sc., and Ph.D. degrees in mathematics from the Faculty of Mathematics and Informatics, Hanoi National University of Education, Vietnam, in 2001, 2004 and 2011, respectively. Dr. Hien began with Hanoi National University of Education in 2001, where he is currently an Associate Professor in mathematics. His current research interests include qualitative theory of differential-difference equations, systems and control theory for complex dynamical systems, time-delay systems, and positve systems. He has published over 70 journal papers.

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Hong, M.T., Van Hien, L. Solvability of L1-induced Controller Synthesis for Positive Systems with Multiple Delays. Int. J. Control Autom. Syst. 19, 3569–3579 (2021). https://doi.org/10.1007/s12555-020-0510-x

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  • DOI: https://doi.org/10.1007/s12555-020-0510-x

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