On stability and stabilizability of positive delay systems
On stability and stabilizability of positive delay systems
The stabilization problem with positivity is investigated in this note for discrete-time linear systems with time delay. A delay-independent necessary and sufficient condition is proposed in terms of linear matrix inequalities (LMIs) for the existence of desired controllers that guarantee the closed-loop system to be asymptotically stable and positive. In addition, the obtained result is further extended to more general case when the system matrices contain uncertain parameters, where a sufficient condition is obtained. The frequently used polytopic parameter uncertainty is taken into consideration. Since the conditions obtained are expressed as LMIs, which can be easily verified by using standard numerical software. A numerical example is provided to illustrate the proposed results
linear matrix inequality (lmi), nonnegative matrix, positive systems, stabilization, time delay
226-234
Wu, Ligang
078c4cdc-89e7-4036-bdbc-75cdf00a97ec
Lam, James
3eea3836-efda-430c-9ad4-ae4f3d4b8c4a
Shu, Zhan
ea5dc18c-d375-4db0-bbcc-dd0229f3a1cb
Du, Baozhu
aaaf0aa4-111f-4912-b78e-bf7a841d5728
March 2009
Wu, Ligang
078c4cdc-89e7-4036-bdbc-75cdf00a97ec
Lam, James
3eea3836-efda-430c-9ad4-ae4f3d4b8c4a
Shu, Zhan
ea5dc18c-d375-4db0-bbcc-dd0229f3a1cb
Du, Baozhu
aaaf0aa4-111f-4912-b78e-bf7a841d5728
Wu, Ligang, Lam, James, Shu, Zhan and Du, Baozhu
(2009)
On stability and stabilizability of positive delay systems.
Asian Journal of Control, 11 (2), .
(doi:10.1002/asjc.99).
Abstract
The stabilization problem with positivity is investigated in this note for discrete-time linear systems with time delay. A delay-independent necessary and sufficient condition is proposed in terms of linear matrix inequalities (LMIs) for the existence of desired controllers that guarantee the closed-loop system to be asymptotically stable and positive. In addition, the obtained result is further extended to more general case when the system matrices contain uncertain parameters, where a sufficient condition is obtained. The frequently used polytopic parameter uncertainty is taken into consideration. Since the conditions obtained are expressed as LMIs, which can be easily verified by using standard numerical software. A numerical example is provided to illustrate the proposed results
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Published date: March 2009
Keywords:
linear matrix inequality (lmi), nonnegative matrix, positive systems, stabilization, time delay
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Mechatronics
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Local EPrints ID: 199749
URI: http://eprints.soton.ac.uk/id/eprint/199749
ISSN: 1561-8625
PURE UUID: 2b7d990a-ee5e-48c0-94d4-098b58ba8f5d
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Date deposited: 20 Oct 2011 10:51
Last modified: 14 Mar 2024 04:17
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Author:
Ligang Wu
Author:
James Lam
Author:
Zhan Shu
Author:
Baozhu Du
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