Journal
INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE
Volume 45, Issue 7, Pages 1496-1507Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/00207721.2013.837545
Keywords
Markovian jump systems; model reduction; incomplete statistics of mode information; linear matrix inequality
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Funding
- National Natural Science Foundation of China [61374031, 61004038]
- National 973 Project of China [2009CB320600]
- Program for New Century Excellent Talents in University [NCET-12-0147]
- Fundamental Research Funds for the Central Universities [HIT.BRETIII.201214]
- Alexander von Humboldt Foundation of Germany
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This paper investigates the problem of H-infinity model reduction for a class of continuous-time Markovian jump linear systems with incomplete statistics of mode information, which simultaneously considers the exactly known, partially unknown and uncertain transition rates. By fully utilising the properties of transition rate matrices, together with the convexification of uncertain domains, a new sufficient condition for H-infinity performance analysis is first derived, and then two approaches, namely, the convex linearisation approach and the iterative approach, are developed to solve the model reduction problem. It is shown that the desired reduced-order models can be obtained by solving a set of strict linear matrix inequalities (LMIs) or a sequential minimisation problem subject to LMI constraints, which are numerically efficient with commercially available software. Finally, an illustrative example is given to show the effectiveness of the proposed design methods.
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