Stability analysis and stabilizing control synthesis via Lyapunov´s second method directly on bond graphs of nonlinear systems

In this paper a set of energy-based methods for the computation of equilibria, the analysis of their stability, and the synthesis of stabilizing control laws are presented. All of them are a transliteration to the bond graph modelling language of methods usually carried out on the state equations of the system. While the computation of equilibrium exploits the circumstance that in such a state no power flows into the storage elements, the methods concerning its stability rely on the fact that, when choosing (a function of) the energy stored in the system as (candidate) Lyapunov function, its orbital derivative can he directly evaluated in terms of the power flow through the bonds of the graph. Armature- and field-voltage control laws for a DC-machine are derived as applications of the methods