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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 653628, 11 pages
Research Article

Optimal Guaranteed Cost Control of a Class of Discrete-Time Nonlinear Systems with Markovian Switching and Mode-Dependent Mixed Time Delays

1Department of Mathematics, Yangzhou University, Yangzhou 225002, China
2Department of Engineering, Faculty of Engineering and Science, University of Agder, 4898 Grimstad, Norway
3School of Computer Science and Technology, Nanjing University of Science and Technology, Nanjing 210094, China

Received 8 May 2013; Accepted 8 June 2013

Academic Editor: Zidong Wang

Copyright © 2013 Yurong Liu 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.


The guaranteed cost control problem is investigated for a class of nonlinear discrete-time systems with Markovian jumping parameters and mixed time delays. The mixed time delays involved consist of both the mode-dependent discrete delay and the distributed delay with mode-dependent lower bound. The associated cost function is of a quadratic summation form over the infinite horizon. The nonlinear functions are assumed to satisfy sector-bounded conditions. By introducing new Lyapunov-Krasovskii functionals and developing some new analysis techniques, sufficient conditions for the existence of guaranteed cost controllers are derived with respect to the given cost function. Moreover, a convex optimization approach is applied to search for the optimal guaranteed cost controller by minimizing the guaranteed cost of the closed-loop system. Numerical simulation is further carried out to demonstrate the effectiveness of the proposed methods.