Journal of Applied Mathematics
Volume 2013 (2013), Article ID 252679, 14 pages
Research Article

Stabilization for Networked Control Systems with Random Sampling Periods

1Institute of Systems Science, Northeastern University, Shenyang 110819, China
2School of Science, Shenyang University of Technology, Shenyang 110870, China
3School of Science, Jilin Normal University, Siping 136000, China
4School of Science, Dalian Jiaotong University, Dalian 116028, China

Received 13 November 2012; Accepted 30 December 2012

Academic Editor: Reinaldo Martinez Palhares

Copyright © 2013 Yuan Li 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.


This paper investigates the stabilization of networked control systems (NCSs) with random delays and random sampling periods. Sampling periods can randomly switch between three cases according to the high, low, and medium types of network load. The sensor-to-controller (S-C) random delays and random sampling periods are modeled as Markov chains. The transition probabilities of Markov chains do not need to be completely known. A state feedback controller is designed via the iterative linear matrix inequality (LMI) approach. It is shown that the designed controller is two-mode dependent and depends on not only the current S-C delay but also the most recent available sampling period at the controller node. The resulting closed-loop systems are special discrete-time jump linear systems with two modes. The sufficient conditions for the stochastic stability are established. An example of the cart and inverted pendulum is given to illustrate the effectiveness of the theoretical result.