This paper develops Lyapunov functions for power systems which have dynamic reactive power loads. These functions are extensions of earlier Lyapunov functions derived for structure preserving power system models having static loads. In order to obtain strict Lyapunov functions, the transient response of the dynamic load must have a logarithmic dependence on voltage. A Lyapunov function is initi...

This paper proposes a novel approach based on Lyapunov function method to analyse the stability of photovoltaic (PV) systems. The Lyapunov function is formulated using the method of quadratic forms, i.e., Krasovskii’s method. The stability of the photovoltaic systems under different operating conditions is analysed based on the formulated Lyapunov function. A comparison of stability analysis us...

In [3] Conley showed that the state-space of a dynamical system can be decomposed into a gradient-like part and a chain-recurrent part, and that this decomposition is characterized by a so-called complete Lyapunov function for the system. In [14] Kalies, Mischaikow, and VanderVorst proposed a combinatorial method to compute discrete approximations to such complete Lyapunov functions. Their appr...

We are interested in iterates of the logistic map T : [0, 1] → [0, 1] defined by

This article deals with some complementarity properties of Z and Lyapunov-like transformations on a symmetric cone. Similar to the results proved for Lyapunov and Stein transformations on Herm(Rn×n), we show that for Lyapunov-like transformations, the P and S properties are equivalent, and that for a Ztransformation, the S-property implies the P-property of a transformation that is (quadratical...