Chin. Phys. B, 2013, Vol. 22(3): 030206    DOI: 10.1088/1674-1056/22/3/030206
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# Stability analysis and control synthesis of uncertain Roesser-type discrete-time two-dimensional systems

Wang Jia (王佳)a, Hui Guo-Tao (会国涛)b, Xie Xiang-Peng (解相朋)b
a School of Mechanical and Vehicular Engineering, Beijing Institute of Technology, Beijing 100081, China;
b School of Information Science and Engineering, Northeastern University, Shenyang 110004, China
Abstract  We study the stability analysis and control synthesis of uncertain discrete-time two-dimensional (2D) systems. The mathematical model of the discrete-time 2D system is established upon the well-known Roesser model, and the uncertainty phenomenon, which appears typically in practical environments, is modeled by a convex bounded (polytope type) uncertain domain. Then, the stability analysis and control synthesis of uncertain discrete-time 2D systems are developed by applying the Lyapunov stability theory. In the processes of stability analysis and control synthesis, the obtained stability/stabilzaition conditions become less conservative by applying some novel relaxed techniques. Moreover, the obtained results are formulated in the form of linear matrix inequalities, which can be easily solved via the standard numerical software. Finally, numerical examples are given to demonstrate the effectiveness of the obtained results.
Keywords:  uncertain two-dimensional systems      Roesser model      Lyapunov stability theory      control synthesis
Received:  06 August 2012      Revised:  05 September 2012      Accepted manuscript online:
 PACS: 02.30.Yy (Control theory) 02.30.-f (Function theory, analysis) 02.40.Ft (Convex sets and geometric inequalities)
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 61104010).
Corresponding Authors:  Wang Jia     E-mail:  wangjiasackville@163.com

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