A Condition for Boundedness of Solutions of Bidimensional Switched Affine Systems With Multiple Foci and Centers

Abstract

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.