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IMA Journal of Mathematical Control and Information 2004 21(4):377-392; doi:10.1093/imamci/21.4.377
© 2004 by Institute of Mathematics and its Applications
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Stabilization and H{infty} control of two-dimensional Markovian jump systems

Huijun Gao1,*, James Lam2, Shengyuan Xu3 and Changhong Wang4

1 Inertial Navigation Center, Harbin Institute of Technology, Room 317, PO Box 1230, Xidazhi Street 92, Harbin, 150001, People's Republic of China, 2 Department of Mechanical Engineering, The University of Hong Kong, Hong Kong, 3 Department of Automation, Nanjing University of Science and Technology, Nanjing 210094, People's Republic of China, 4 Inertial Navigation Center, Harbin Institute of Technology, Room 317, PO Box 1230, Xidazhi Street 92, Harbin, 150001, People's Republic of China

This paper extends the results obtained for one-dimensional Markovian jump systems, to investigate the problems of stochastic stabilization and H{infty} control of two-dimensional (2D) systems with Markovian jump parameters. The mathematical model of 2D jump systems is established upon the well-known Roesser model, and sufficient conditions are obtained for the existence of desired controllers in terms of linear matrix inequalities, which can be readily solved by available numerical software. These obtained results are further extended to more general cases whose system matrices also contain parameter uncertainties represented by either polytopic or norm-bounded approaches. A numerical example is provided to show the applicability of the proposed theories.

Keywords: 2D system; H{infty} control; linear matrix inequality; Markovian jump system; stochastic stabilization.

Received 15 July 2003.

* Email: hjgao{at}hit.edu.cn.


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