A new approach based on the discriminant system of polynomial for robust stability and stabilization of two-dimensional systems |
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| Authors: | Xiaoxue Li Xiaorong Hou |
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| Institution: | 1. Hangzhou Innovation Institute, Beihang University, 310051, Hangzhou, China;2. School of Automation Science and Electrical Engineering, Beihang University, 100191, China;1. The Key Laboratory of Autonomous Systems and Network Control, Ministry of Education, School of Automatic Science and Engineering, South China University of Technology, Guangzhou 510641, China;2. Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, School of Mathematics and Information Sciences, Henan Normal University, Xinxiang, Henan 453007, China;1. Key Laboratory of Dependable Service Computing in Cyber Physical Society of Ministry of Education, Chongqing University, Chongqing 400044, China;2. College of Automation, Chongqing University, Chongqing 400044, China;3. Public Security Business Group of Gosuncn Technology Group Co.,Ltd., China, 510530;1. Institute of Automation, Qufu Normal University, Qufu, Shandong 273165, PR China;2. Department of Systems Naval Mechatronic Engineering, National Cheng Kung University, Tainan, Taiwan;3. College of Engineering, Qufu Normal University, Rizhao, Shandong 276826, PR China;1. Systems Engineering Department, KFUPM, Dhahran 31261, Saudi Arabia;2. School of Automation, Beijing Institute of Technology, Beijing, China |
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| Abstract: | In this paper, we present necessary and sufficient stability and robust stability conditions for two-dimensional (2D) systems described by the Fornasini-Marchesini (FM) second model in terms of the discriminant systems of polynomial. This paper simplifies the traditional method of stability into a tractable method by the fractional linear transformation (FLT). More specifically, we reduce the stability analysis to a easy issue whether some polynomials are positive definite. Then we use the same idea to consider the stabilization and robust stabilization issues. Finally, the effectiveness of the proposed results is demonstrated by a practical example and two numerical examples. |
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