We present a study of the transfer of satellites between elliptic Keplerian orbits using Lyapunov stability theory specific to this problem. The construction of Lyapunov functions is based on the fact that a non-degenerate Keplerian orbit is uniquely described by its angular momentum and Laplace (Runge-Lenz) vectors. We suggest a Lyapunov function, which gives a feedback controller such that th...

This paper presents Lyapunov functions for proving stability of steady gliding motions for vehicles with hydrodynamic or aerodynamic forces and moments. Because of lifting forces and moments, system energy cannot be used as a Lyapunov function candidate. A Lyapunov function is constructed using a conservation law discovered by Lanchester in his classical work on phugoid-mode dynamics of an airp...

In this paper we introduce some stability criteria for impulsive fuzzy system of differential equations with finite delay in states. Firstly, a new comparison principle for fuzzy differential system compared to crisp ordinary differential equation, based on a notion of upper quasi-monotone nondecreasing, in N dimentional state space is presented. Furthermore, in order to analyze the stability o...

This research work investigates the global chaos synchronization of identical chaotic systems based on sliding mode control theory and Lyapunov stability theory. The paper begins with a problem statement on global chaos synchronization of chaotic systems. A general result is derived for the global chaos synchronization of chaotic systems using slide mode control and this result is established u...

In this letter, the problem of robust stabilization of a class of nonlinear dynamical systems with delayed perturbations is considered. Based on the stability of the nominal systems, a new stabilizing control law for exponential stability of the system is designed using Lyapunov stability theory. c © 2003 Elsevier B.V. All rights reserved.

This paper presents some new analytical results on the global stability for a general class of discretetime state-space neural networks by using the Lyapunov stability theory and the contraction mapping theorem. The proposed stability conditions are determined by the synaptic weights matrices of the neural network.

In a companion paper ('Explicit construction of quadratic Lyapunov functions for the small gain, positivity, circle, and Popov theorems and their application to robust stability. Part I: Continuous-time theory'), Lyapunov functions were constructed in a unified framework to prove sufficiency in the small gain, positivity, circle, and Popov theorems. In this Part II, analogous results are develo...

Correctness of many hybrid and distributed systems require stability and convergence guarantees. Unlike the standard induction principle for verifying invariance, a theory for verifying stability or convergence of automata is currently not available. In this paper, we formalize one such theory proposed by Tsitsiklis [25]. We build on the existing PVS metatheory for untimed, timed, and hybrid in...

The study of the stability properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems. The objective of this paper is to outline some of these problems, to review progress made in solving these problems in a number of diverse communities , and to review some problems that remain open. An important contribution of our work is to bring to...

Some theoretical investigations of large angle attitude manoeuvres have been based on the app l i ca ti on of Lyapunov' s stability theory. With this method r1ortensen derived stable control laws for performing attitude manoeuvres with either thrusters or reaction wheels. Previous results were idealized in that they i qnored the non l i neari ti es inherent in the opera ti on of both types of a...