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 present a method of approximating the unique invariant measure and associated Lyapunov exponents of a random dynamical system deened by the iid composition of a family of maps in situations where only one Lyapunov exponent is observed. As a corollary, our construction also provides a method of estimating the top Lyapunov exponent of an iid random matrix product. We develop rigorous numerical...

Lyapunov functions are an important tool to determine the basin of attraction of exponentially stable equilibria in dynamical systems. In Marinosson (2002), a method to construct Lyapunov functions was presented, using finite differences on finite elements and thus transforming the construction problem into a linear programming problem. In Hafstein (2004), it was shown that this method always s...

A qualitative method is explored for analyzing the stability of systems. The approach is a generalization of the celebrated Lyapunov method. Whereas classically, the Lyapunov method is based on the simple comparison theorem, deriving suitable candidate Lyapunov functions remains mostly an art. As a result, in the realm of delay equations, such Lyapunov methods can be quite conservative. The gen...

Abstract: The paper presents a method of determining the Lyapunov quadratic functional for linear time-invariant system with knon-commensurate neutral type time delays. The Lyapunov functional is constructed for its given time derivative, which is calculated on the trajectory of the system with k-non-commensurate neutral type time delays. The presented method gives analytical formulas for the c...

-This study addresses a fuzzy Lyapunov method for the stability analysis of time-delay fuzzy systems subject to external disturbances. The Takagi-Sugeno (T-S) fuzzy model and parallel distributed compensation (PDC) scheme are first employed to design a nonlinear fuzzy controller in order to stabilize the time-delay fuzzy systems. According to the controlled system, the H infinity criterion is d...

This paper develops a novel method to deal with the stability problem of sampled-data systems. The multiple Lyapunov function method used in switched systems is extended to sampled-data systems and a multiple Lyapunov functional method is developed for nonlinear sampled-data systems. An application is presented where two different Lyapunov functionals are constructed in order to determine the s...

The fuzzy Lyapunov method is investigated for use with a class of interconnected fuzzy systems. The interconnected fuzzy systems consist of J interconnected fuzzy subsystems, and the stability analysis is based on Lyapunov functions. Based on traditional Lyapunov stability theory, we further propose a fuzzy Lyapunov method for the stability analysis of interconnected fuzzy systems. The fuzzy Ly...