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Abstract and Applied Analysis
Volume 2014, Article ID 938781, 16 pages
http://dx.doi.org/10.1155/2014/938781
Research Article

Robust Finite-Time Control for Nonlinear Markovian Jump Systems with Time Delay under Partially Known Transition Probabilities

Institute of Automation, Qufu Normal University, Qufu, Shandong 273165, China

Received 7 November 2013; Accepted 7 December 2013; Published 20 February 2014

Academic Editor: Hao Shen

Copyright © 2014 Dong Yang and Guangdeng Zong. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper is concerned with the problem of robust finite-time control for a class of nonlinear Markovian jump systems with time delay under partially known transition probabilities. Firstly, for the nominal nonlinear Markovian jump systems, sufficient conditions are proposed to ensure finite-time boundedness, finite-time boundedness, and finite-time state feedback stabilization, respectively. Then, a robust finite-time state feedback controller is designed, which, for all admissible uncertainties, guarantees the finite-time boundedness of the corresponding closed-loop system. All the conditions are presented in terms of strict linear matrix inequalities. Finally a numerical example is provided to demonstrate the effectiveness of all the results.