LP approach to exponential stabilization of singular linear positive time-delay systems via memory state feedback

Nguyen H. Sau; Vu N. Phat

doi:10.3934/jimo.2017061

Article Contents

2018, Volume 14, Issue 2: 583-596. Doi: 10.3934/jimo.2017061

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LP approach to exponential stabilization of singular linear positive time-delay systems via memory state feedback

Nguyen H. Sau^1, and
Vu N. Phat^2,

1.
Department of Mathematics, Electric Power University, 235 Hoang Quoc Viet Road, Hanoi, Vietnam
2.
Institute of Mathematics, VAST, 18 Hoang Quoc Viet Road, Hanoi, Vietnam

Received: October 2016

Revised: January 2017

Early access: June 2017

Published: April 2018

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Abstract

This paper deals with the exponential stabilization problem by means of memory state feedback controller for linear singular positive systems with delay. By using system decomposition approach, singular systems theory and Lyapunov function method, we obtain new delay-dependent sufficient conditions for designing such controllers. The conditions are given in terms of standard linear programming (LP) problems, which can be solved by LP optimal toolbox. A numerical example is given to illustrate the effectiveness of the proposed method.

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Mathematics Subject Classification: Primary: 93D20, 34D20; Secondary: 37C75.

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Figure 1. State response of the closed-loop system

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