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

What is it about?

Different subsystems of a switched system have different equilibria just like different individuals of a social group have different objects/opinions. If individual subsystems have different equilibria, the behaviors of switched systems are more different than that of switched systems with a common single equilibrium point. This paper explains some main properties of such systems' behaviors.

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Why is it important?

Due to differences of subsystems' equilibira, such a switched system doesn't tend to any of its subsystems' multiple equilibria as time goes to infinity if there always exist switchings among subsystems. The results obtained in this paper imply that every individuals in a hybrid system cannot reach their own object/opinion but a region. The importance of the obtained results show that under suitable conditions, even every subsystem has an unstable equilibrium point, the whole switched system tends to a region as time goes to infinity.