The linear stability properties of viscous circular flows in a rotating environment are studied with respect to symmetric perturbations. Through the use of an effective energy or Lyapunov functional, we derive sufficient conditions for Lyapunov stability with respect to such perturbations. For circular flows with swirl velocity V (r) we find that Lyapunov stability is determined by the properti...

We examine the stability of two interfering pro essors with servi e rates depending on the number of users present of ea h of the lasses and subje t to stati or dynami load balan ing. Su h models arise in several ontexts, espe ially in wireless networks, or multipro essing. In ase of stati load balan ing, we extend existing stability results by deriving Lyapunov fun tions that are onne ted to t...

Partial state variables stabilization control of uncertain nonlinear systems is developed for chaos systems synchronization control. Response systems are constructed for uncertain Rössler systems. In order to make response systems track the drive systems asymptotically stable, error systems with uncertain and nonlinear factors are designed. Using partial state stability theory of nonlinear syst...

The method of Lyapunov functions (Lyapunov's second or direct method) was originally developed for studying the stability of a xed point of an autonomous or non-autonomous diierential equation. It was then extended from xed points to sets, from diierential equations to dynamical systems and to stochastic diierential equations. We go one step further and develop Lyapunov's second method for rand...

*Correspondence: [email protected] School of Mathematical Science, Anhui University, Hefei, P.R. China Abstract In this paper, using the theory of q-fractional calculus, we deal with the q-Mittag-Leffler stability of q-fractional differential systems, and based on it, we analyze the direct Lyapunov method of q-fractional differential systems. Several sufficient criteria are established to guaran...

A nonlinear feedback path controller for a differential drive mobile robot is presented in this paper. First, a kinematic model in error coordinates expressed in a moving reference frame partially linked to the robot is developed. The control law is designed using backstepping method yielding exponential stability of the closed-loop system. Stability analysis is performed via Lyapunov stability...

In this paper we consider the dynamics of solutions of impulsive differential equations with fixed time moments of impulsive effects on the basis of comparison methods and vector Lyapunov functions. We propose sufficient conditions on the following dynamic properties: stability, attractivity, and some combinations of them.

The aim of this paper is to design a law control of a nonlinear web winding system using the Lyapunov stability theory. The Lyapunov function is a powerful tool for the stability analysis of nonlinear dynamic systems. This system knows several constraints such as the thermal effects caused by the frictions, and the mechanical effects provoked by metal elongation, that generates dysfunctions due...

Differential equations with impulsive effect provide mathematical models for many phenomena and processes in the field of natural sciences and technology. Recently a well developed stability theory of functional differential systems has come into existence [15-21]. Qualitative properties of impulsive differential equations have been intensively researched for years. In [3-11], by using lyapunov...

Motivated by the fact that delay difference inclusions (DDIs) form a rich modeling class that includes, for example, uncertain time-delay systems and certain types of networked control systems, this paper provides a comprehensive collection of Lyapunov methods for DDIs. Firstly, the Lyapunov-Krasovskii approach, which is an extension of the classical Lyapunov theory to time-delay systems, is co...