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Observer‐based finite‐time stabilization for extended Markov jump systems
Author(s) -
Luan Xiaoli,
Liu Fei,
Shi Peng
Publication year - 2011
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.262
Subject(s) - control theory (sociology) , observer (physics) , linear matrix inequality , mathematics , controller (irrigation) , convex optimization , markov process , norm (philosophy) , bounded function , markov chain , regular polygon , mathematical optimization , computer science , control (management) , law , statistics , mathematical analysis , physics , geometry , quantum mechanics , artificial intelligence , political science , agronomy , biology
In this paper, we study the problem of observer‐based finite‐time stabilization for a class of extended Markov jump systems with norm‐bounded uncertainties and external disturbances. The stochastic character under consideration is governed by a finite‐state Markov process, but with only partial information on the transition jump rates. Based on the finite‐time stability analysis, sufficient conditions for the existence of the observer‐based controller are derived via a linear matrix inequality approach such that the closed‐loop system trajectory stays within a prescribed bound in a fixed time interval. When these conditions are satisfied, the designed observer‐based controller gain matrices can be obtained by solving a convex optimization problem. Simulation results demonstrate the effectiveness of the approaches proposed in this paper.Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society