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L1-induced norm and controller synthesis of positive systems

L1-induced norm and controller synthesis of positive systems
L1-induced norm and controller synthesis of positive systems
In this paper, the problem of ?1?1-induced controller design for discrete-time positive systems is investigated with the use of linear Lyapunov function. An analytical method to compute the exact value of ?1?1-induced norm is first presented. Then, a novel characterization for stability and ?1?1-induced performance is proposed. Based on the characterization, a necessary and sufficient condition for the existence of desired controllers is derived, and an iterative convex optimization approach is developed to solve the condition. In addition, the synthesis of the state-feedback controller for single-input multiple-output (SIMO) positive systems is investigated. For this special case, an analytic solution is established to show how the optimal ?1?1-induced controller can be designed, and some links to the spectral radius of the closed-loop systems are provided. Finally, the theoretical results are illustrated through a numerical example.
iterative algorithm, linear lyapunov functions, ?1?1-induced performance, positive systems
0005-1098
1377-1385
Chen, Xiaoming
593009e9-709e-42d5-b6f3-4adaef0cefc0
Lam, james
3eea3836-efda-430c-9ad4-ae4f3d4b8c4a
Li, Ping
84293437-7ab4-4c22-b68b-937bfc57ee15
Shu, Zhan
ea5dc18c-d375-4db0-bbcc-dd0229f3a1cb
Chen, Xiaoming
593009e9-709e-42d5-b6f3-4adaef0cefc0
Lam, james
3eea3836-efda-430c-9ad4-ae4f3d4b8c4a
Li, Ping
84293437-7ab4-4c22-b68b-937bfc57ee15
Shu, Zhan
ea5dc18c-d375-4db0-bbcc-dd0229f3a1cb

Chen, Xiaoming, Lam, james, Li, Ping and Shu, Zhan (2013) L1-induced norm and controller synthesis of positive systems. Automatica, 49 (5), 1377-1385. (doi:10.1016/j.automatica.2013.02.023).

Record type: Article

Abstract

In this paper, the problem of ?1?1-induced controller design for discrete-time positive systems is investigated with the use of linear Lyapunov function. An analytical method to compute the exact value of ?1?1-induced norm is first presented. Then, a novel characterization for stability and ?1?1-induced performance is proposed. Based on the characterization, a necessary and sufficient condition for the existence of desired controllers is derived, and an iterative convex optimization approach is developed to solve the condition. In addition, the synthesis of the state-feedback controller for single-input multiple-output (SIMO) positive systems is investigated. For this special case, an analytic solution is established to show how the optimal ?1?1-induced controller can be designed, and some links to the spectral radius of the closed-loop systems are provided. Finally, the theoretical results are illustrated through a numerical example.

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More information

e-pub ahead of print date: 18 March 2013
Published date: May 2013
Keywords: iterative algorithm, linear lyapunov functions, ?1?1-induced performance, positive systems
Organisations: Mechatronics

Identifiers

Local EPrints ID: 354865
URI: https://eprints.soton.ac.uk/id/eprint/354865
ISSN: 0005-1098
PURE UUID: e8cda97f-57e9-428e-9023-4a07266967cc
ORCID for Zhan Shu: ORCID iD orcid.org/0000-0002-5933-254X

Catalogue record

Date deposited: 29 Jul 2013 13:41
Last modified: 06 Jun 2018 12:30

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