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On the Boundary of the Attraction Basin in a Class of Piecewise Linear Systems |
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| Authors: | Yuhong Zhang Weisheng Huang Xiaosong Yang |
| Affiliation: | School of Mathematics and Statistics, South-Central Minzu University, Wuhan, Hubei 430074, China;MOE Key Laboratory of Fundamental Physical Quantities Measurement, Hubei Key Laboratory of Gravitation and Quantum Physics, PGMF, School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China; School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China; Hubei Key Laboratory of Engineering Modeling and Science Computing, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China |
| Abstract: | In this paper, we investigate the boundary of the attraction basin of a class of piecewise linear systems arising from anti-stable linear systems with saturated linear state feedback. In three-dimensional cases, for this class of systems, we prove that the equilibrium points other than the origin lie on the boundary of the attraction basin of the origin. This gives strong evidence that the boundary of the attraction basin is homeomorphic to a sphere. Some examples are provided to illustrate the results. |
| Keywords: | Piecewise linear system boundary of attraction basin index saturated state feedback |
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