On the Stability of a Class of Switched Bond Graphs

This paper deals with the stability analysis of a class of switched bond graphs where all the storage components remain unchanged and in integral causality under mode switching. These properties assure the existence of a unique energy function common to all the switching modes, and the non occurrence of state jumps or discontinuities in the switched system trajectories. A result on stability of equilibria in the sense of Lyapunov is presented. The derivation of this result is done using a bond graph technique for Lyapunov stability analysis (previously developed by one of the authors of this paper) in association with results available in the literature related to the satisfaction by a candidate Lyapunov function of a sequence nonincreasing condition for the state trajectories of a general autonomous switched system. Because of its versatility, the Switched Power Junction formalism is chosen in this paper to model and simulate the commutations in the bond graph domain.