Lyapunov Stability of pseudo Euler-Lagrange systems

This paper presents a systematic approach to find a Lyapunov function for stability analysis of pseudo Euler-Lagrange systems. There are two main contributions of this paper. First, a systematic procedure is proposed to obtain a Lyapunov function for the system directly from the mathematical structure of the differential equations, without the need to determine any kinetic or potential energy of the system first. Second, energy-based ideas used in Euler-Lagrange systems are extended to the case where generalized velocity variables are not necessarily the derivative of generalized position variables. The method proposed here works for any mathematical model in the class of pseudo Euler-Lagrange systems and is therefore not restricted to models of physical systems, having thus the potential to address economic, biologic and other systems. Several examples illustrate the application of the new approach.