# Dissipative Controller Design for Networked Control Systems via the Markovian Jump System Approach

## DOI:

https://doi.org/10.5614/j.eng.technol.sci.2013.45.1.3## Abstract

This paper describes a dissipative controller design for networked control systems modeled by the Markovian jump system. Dissipativity refers to the existence of a supply rate dealing with the system such that the closed-loop system has a dissipative property. The main result of this paper is a solvability condition in terms of linear matrix inequalities for achieving dissipativity of a dynamic output feedback problem in networked control systems via the Markovian jump system approach. A numerical example is given to show the efficacy of the proposed design.### Downloads

## References

Hokayem, P.F. & Abdallah C.T., Inherent Issues in Networked Control Systems: A Survey, Proc. of the 2004 American Control Conference, pp. 4897-4902, June 30-July 2, 2004.

Gupta, R.A. & Chow, M.Y., Networked Control Systems: Overview and Research Trends, IEEE Trans. on Industrial Electronics, 57(7), pp. 2527-2535, July 2010.

Heemels, W.P.M.H. & van de Wouw, N., Stability and Stabilization of Networked Control Systems, in Networked Control Systems, Bemporad, A., et al. (eds), Springer Verlag Berlin, pp. 203-253, 2010.

Heemels, W.P.M.H, Teel, A.R., van de Wouw, N. & Nesic, D., Networked Control Systems with Communication Constraints: Tradeoffs between Transmission Intervals, Delays and Performance, IEEE Trans. Automatic Control, 55(8), pp. 1781-1796, August 2010.

Hespanha, J.P., Naghshtabrizi, P. & Xu, Y., A Survey of Recent Results in Networked Control Systems, Proceedings of the IEEE, 95(1), pp. 138-162, January 2007.

Lam, J., Gao, H. & Wang, C., Stability Analysis for Continuous Systems with Two Additive Time Varying Delay Components, Systems and Control Letters, 56(1), pp. 16-24, January 2007.

Gao, H., Chen, T. & Lam, J., A New Delay System Approach to Network-based Control, Automatica, 44(1), pp. 39-52, January 2008.

Shi, Y. & Yu, B., Output Feedback Stabilization of Networked Control Systems with Random Delays Modeled by Markov Chains, IEEE Trans. on Automatic Control, 54(7), pp. 1668-1674, July 2009.

Aberkane, S., Ponsart, J.C. & Sauter, D., Output-Feedback H2/Ha?? Control of A Class of Networked Fault Tolerant Control Systems, Asian Journal of Control , 10(1), pp. 34-44, January 2008.

Hirche, S., Chen, C-C. & Buss, M., Performance Oriented Control Over Networks: Switching Controllers and Switched Time Delay, Asian Journal of Control, 10(1), pp. 24-33, January 2008.

Ishii, H., Ha?? Control with Limited Communication and Message Loss, Systems and Control Letters, 57, pp. 322-331, 2008.

Peng, C. & Tian, Y-C., Network-based Ha?? Control of Linear Systems with State Quantization, Journal of Information Sciences, 177(24), pp. 5763-5774, 2007.

Xiao, N., Xie, L. & Fu, M., Quantized Stabilization of Markov Jump Linear Systems via State Feedback, IEEE American Control Conf., pp. 4020-4025, June 10-12, 2009.

Zhang, W., Branicky, M.S. & Phillips, S.M., Stability of Networked Control Systems, IEEE Control Systems Magazine, 21(2), pp. 84-99, 2001.

Costa, O.L.V., Fragoso, M.D. & Marques, R.P., Discrete-Time Markov Jump Linear Systems, Springer-Verlag, London, UK, 2005.

Li, L. & Ugrinovskii, V.A., On Necessary and Sufficient Conditions for Ha?? Output Feedback Control of Markov Jump Linear Systems, IEEE Trans. on Automatic Control, 52(7), pp. 1287-1292, July 2007.

Fioravanti, A.R., Goncalves, A.P.C. & Geromel, J.C., H2 and Ha?? Filtering of Discrete-time Markov Jump Linear Systems through Linear Matrix Inequalities, Proceedings of the 17th World Congress The International Federation of Automatic Control Seoul, Korea, pp. 2681-2688, July 6-11, 2008.

Geromel, J. C., Goncalves, A.P.C. & Fioravanti, A.R., Dynamic Output Feedback Control of Discrete-Time Markov Jump Linear Systems through Linear Matrix Inequalities, SIAM Journal on Control and Optimization, 48(2), pp. 573-593, 2009.

Aliyu, M.D.S. & Boukas, E.K., Robust H-infinity Control for Markovian Jump Nonlinear Systems, Journal of Mathematical Control and Information, 17, pp. 295-308, 2000.

Xiong, J. & Lam, J., Robust H2 Control of Markovian Jump Systems with Uncertain Switching Probabilities, International Journal of Systems Science, 40(3), pp. 255-265, March 2009.

Seiler, P. & Sengupta, R., An Ha?? Approach to Networked Control, IEEE Trans. on Automatic Control, 50(3), pp. 356-364, March 2005.

Willems, J.C., Dissipative Dynamical Systems Part I: General Theory, Part II: Linear Systems with Quadratic Supply Rates, Arch. Rtion. Mech. Analysis, 45, pp. 321-393, 1972.

Brogliato, B., Lozano, R., Maschke, B. & Egeland, O., Dissipative Systems Analysis and Control, Springer-Verlag, London, 2007.

Aliyu, M.D.S., Dissipativity and Stability of Nonlinear Jump Systems, Proc. of American Control Conference, pp. 795-799, June 1999.

Zhang, H., Yan, H. & Chen, Q., Stability and Dissipative Analysis for A Class of Stochastic System with Time-Delay, Journal of the Franklin Institute, 347, pp. 882-893, June 2010.

Mahmoud, M.S., Nounou, H.N. & Xia, Y., Robust Dissipative Control for Internet-Based Switching Systems, Journal of the Franklin Institute, 347(1), pp. 154-172, February 2010.

Zhang, H., Guan, Z-H. & Feng, G., Reliable Dissipative Control for Stochastic Impulsive Systems, Automatica, 44(2008), pp. 1004-1010, 2008.

Wang, J., Han, Q.L. & Yang, F., Robust Dissipative Control for Networked Control Systems with Multiple Packet Dropout, Proc. of the 18th IFAC World Congress, pp. 78-83, August 28-Sept. 2, 2011.

Najmurrokhman, A., Riyanto, B., Rohman, A.S. & Ortega, R., Output Feedback Controller for Dissipative Networked Control Systems Via Markovian Jump System Approach, Proceedings of International Conference on Intelligent Unmanned Systems (ICIUS), Bali, Indonesia, pp. 510-515, Nov 3-5, 2010.

El Hawwary, M.I., Passivity Methods for The Stabilization of Closed Sets in Nonlinear Control Systems, PhD Dissertation, Dept. of Electrical and Computer Engineering, University of Toronto, 2011.

Goncalves, A.P.C., Fioravanti, A.R. & Geromel, J.C., Filtering for Discrete-Time Markov Jump Systems with Network Transmitted Mode, 49th IEEE Conference on Decision and Control, pp. 924-929, Dec. 15-17, 2010.

## Downloads

## Published

## How to Cite

*Journal of Engineering and Technological Sciences*,

*45*(1), 25-46. https://doi.org/10.5614/j.eng.technol.sci.2013.45.1.3