Model transformation based sliding mode control of discrete-time two-dimensional Fornasini–Marchesini systems |
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| Authors: | Rongni Yang Wei Xing Zheng |
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| Institution: | 1. School of Computing, Engineering and Mathematics, Western Sydney University, Sydney, NSW 2751, Australia;2. School of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, China |
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| Abstract: | This paper investigates the problem of sliding mode control (SMC) for discrete-time two-dimensional (2-D) systems subject to external disturbances. Given a 2-D Fornasini–Marchesini (FM) local state space model, attention is focused on designing the 2-D sliding surface and sliding mode controller, which guarantees the resultant closed-loop system to be asymptotically stable. Particularly, this problem is solved using the model transformation based method. First of all, sufficient conditions are formulated for the existence of a linear sliding surface guaranteeing the asymptotic stability of the equivalent sliding mode dynamics. Based on this, a sliding mode controller is synthesized to ensure that the associated 2-D FM system satisfies the reaching condition. The efficiency of the proposed 2-D SMC law design is shown by a numerical example. This paper extends the idea of model transformation to the 2-D systems and solves the SMC problem of a more general 2-D model in FM type for the first time. |
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| Keywords: | Corresponding author |
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