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Journal of Control Science and Engineering
Volume 2015 (2015), Article ID 140527, 11 pages
http://dx.doi.org/10.1155/2015/140527
Research Article

Model Predictive Control for Continuous-Time Singular Jump Systems with Incomplete Transition Rates

Key Laboratory for Advanced Process Control of Light Industry of the Ministry of Education, School of Internet of Things Engineering, Jiangnan University, Wuxi 214122, China

Received 4 May 2015; Revised 12 July 2015; Accepted 21 July 2015

Academic Editor: Petko Petkov

Copyright © 2015 Xinxin Gu et al. 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 model predictive control (MPC) problem for continuous-time Markov Jump Systems (MJSs) with incomplete transition rates and singular character. Sufficient conditions for the existence of a model predictive controller, which could optimize a quadratic cost function and guarantee that the system is piecewise regular, impulse-free, and mean square stable, are given in two cases at each sampling time. Since the MPC strategy is aggregated into continuous-time singular MJSs, a discrete-time controller is employed to deal with a continuous-time plant and the cost function not only refers to the singularity but also considers the sampling period. Moreover, the feasibility of the MPC scheme and the mean square admissibility of the closed-loop system are deeply discussed by using the invariant ellipsoid. Finally, a numerical example is given to illustrate the main results.