STRICT LYAPUNOV FUNCTION AND CHETAEV FUNCTION FOR STABILITY/INSTABILITY ANALYSIS OF THE PENDULUM

摘要

Stability analysis of nonlinear systems can be carried out by the Lyapunov’s first method (linearization technique). However, by utilizing this approach most insight about the physical system may be lost. Alternative approaches are available to exploit system characteristics such as those associated to energy concepts for stability and instability analysis. In this paper, with reference to a simple nonlinear system –the pendulum–, we proposed first, a simple strict Lyapunov function motivated by energy consideration to study asymptotic stability of some equilibria, and second a Chetaev function to analyze instability of the remaining ones. A remarkable point is that both functions have a common structure based on the system’s energy, and differs only in a single scalar parameter.