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A Condition for Boundedness of Solutions of Bidimensional Switched Affine Systems With Multiple Foci and Centers
Author(s) -
Zhu Liying
Publication year - 2018
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.1535
Subject(s) - affine transformation , control theory (sociology) , exponential stability , mathematics , focus (optics) , pairwise comparison , stability (learning theory) , path (computing) , control (management) , computer science , nonlinear system , pure mathematics , physics , statistics , quantum mechanics , artificial intelligence , machine learning , optics , programming language
This paper studies boundedness of solutions of bidimensional switched affine linear systems. Every subsystem of the systems has a single stable/ unstable focus/ center and all the equilibria pairwise differ. By using the multiple polar coordinate systems method, this paper proposes a condition of boundedness of solutions of such switched systems under periodic/ quasi‐periodic switching paths. The condition is also shown a sufficient condition of global asymptotic region stability of such switched systems with respect to a region containing all multiple equilibria. A global asymptotic region‐stabilizing control, a periodic/ quasi‐periodic switching path, and a corresponding algorithm are all designed for such switched control systems. An illustrative example demonstrates the effectiveness and practicality of our new results.