Region stability of switched two-dimensional linear dissipative Hamiltonian systems with multiple equilibria

Abstract

This paper studies the issues of region stability of switched two-dimensional linear dissipative Hamiltonian systems. Such switched systems are composed of two stable subsystems with two different equilibrium points. Since the equilibrium points of two subsystems are different, and the state matrices of subsystems may not commute, it is difficult to address such switched systems. This paper considers the case that the switching path corresponding to the switched systems is a switching line passing through the equilibrium points of two different subsystems. A suitable region containing all the equilibrium points of subsystems is first determined. Based on the concept of region stability of switched systems with multiple equilibrium points, this paper proposes some sufficient conditions of region stability and asymptotically region stability for such kind of switched linear dissipative Hamiltonian systems via the maximum energy function method. The above main results obtained can be applied to some classes of electronic circuits, such as switching DC/DC converters and AC/DC converters. As an application and illustration, a switching DC circuit and two numerical examples are carried out to show the effectiveness of the region stability results obtained in this paper.