A Generalized Nonuniform Contraction and Lyapunov Function

Nonuniform power instability and Lyapunov sequences

The aim of this paper is to present necessary and sufficient conditions for nonuniform power instability property of linear discrete-time systems in Banach spaces. A characterization of the nonuniform power instability in terms of Lyapunov sequences is also given.

Generalized Lyapunov Function for Stability Analysis of Uncertain Systems

An alternative approach for stability analysis of uncertain systems modelled in statespace is suggested. A new candidate for Lyapunov function and based on it stability condition which generalize most of the available results in the field are presented. The applicability of this approach is illustrated by an example, treated many times by different approaches. Copyright 2005 IFAC

Coupled fixed points of generalized Kanann contraction and its applications

The purpose of this paper is to find of the theoretical results of fixed point theorems for a mixed monotone mapping in a metric space endowed with partially order by using the generalized Kanann type contractivity of assumption. Also, as an application, we prove the existence and uniqueness of solution for a first-order ordinary differential equation with periodic bou...

A note on norm-based Lyapunov functions via contraction analysis

It is well know that for globally contractive autonomous systems, there exists a unique equilibrium and the distance to the equilibrium evaluated along any trajectory decreases exponentially with time. We show that, additionally, the magnitude of the velocity evaluated along any trajectory decreases exponentially, thus giving an alternative choice of Lyapunov function. 1 Main Result Consider th...

SOLVING A CLASS OF GENERALIZED LYAPUNOV OPERATOR DIFFERENTIAL EQUATIONS WITHOUT THE EXPONENTIAL OPERATOR FUNCTION A bstract