In this article, an engineering/physical dynamic system including losses is analyzed inrelation to the stability from an engineer’s/physicist’s point of view. Firstly, conditions for a Hamiltonian to be an energy function, time independent or not, is explained herein. To analyze stability of engineering system, Lyapunov-like energy function, called residual energy function is used. The residual function may contain, apart from external energies, negative losses as well. This function includes the sum of potential and kinetic energies, which are special forms and ready-made (weak) Lyapunov functions, and loss of energies (positive and/or negative) of a system described in different forms using tensorial variables. As the Lypunov function, residual energy function is defined as Hamiltonian energy function plus loss of energies and then associated weak and strong stability are proved through the first time-derivative of residual energy function. It is demonstrated how the stability analysis can be performed using the residual energy functions in different formulations and in generalized motion space when available. This novel approach is applied to RLC circuit, AC equivalent circuit of Gunn diode oscillator for autonomous, and a coupled (electromechanical) example for nonautonomous case. In the nonautonomous case, the stability criteria can not be proven for one type of formulation, however, it can be proven in the other type formulation.

The purpose of that paper is to develop of unified equations of electromechanical energy converters accounting for the magnetic non-linearity of the main magnetic circuit of a converter. The concept of applying higher order forms of winding currents for the description of the co-energy function is introduced in order to derive the structure of converter equations via mathematical analysis. Also, another concept of equivalent magnetizing currents is applied to determine the higher order forms for selected converters designs. The structure of circuital equations for converters with multiple windings has been unified by means of the introduction of matrices of dynamic and nonlinear inductances following the higher order forms of the co-energy function.