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Discrete Dynamics in Nature and Society
Volume 2017, Article ID 3256871, 11 pages
https://doi.org/10.1155/2017/3256871
Research Article

Finite-Time Passivity and Passification Design for Markovian Jumping Systems with Mode-Dependent Time-Varying Delays

School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China

Correspondence should be addressed to Chao Ma; nc.ude.btsu@amc

Received 29 September 2016; Revised 8 February 2017; Accepted 16 February 2017; Published 7 March 2017

Academic Editor: Chuanxi Qian

Copyright © 2017 Chao Ma. 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 investigates the finite-time passivity and passification design problem for a class of Markovian jumping systems with mode-dependent time-varying delays. By employing the Lyapunov-Krasovskii functional method, delay-dependent sufficient criteria are derived to ensure the mean-square stochastically finite-time passivity. Based on the established results, mode-dependent passification controller is further designed in terms of linear matrix inequalities, such that the prescribed passive performance index of the resulting closed-loop system can be satisfied. Finally, two illustrative examples are given to show the effectiveness of the obtained theoretical results.