An efficient and numerically stable method to determine all the Lyapunov characteristic exponents of a dynamical system is developed. Numerical experiments are presented highlighting some aspects of convergence, accuracy and efficiency in the computation of the Lyapunov characteristic exponents. PACS Codes: 05.45.+b, 02.70.-C

This note presents a stability analysis method for piecewise discrete-time linear systems based on a piecewise smooth Lyapunov function. It is shown that the stability of the system can be established if a piecewise Lyapunov function can be constructed and, moreover, the function can be obtained by solving a set of linear matrix inequalities (LMIs) that is numerically feasible with commercially...

The transfer matrix method is applied to quasi one-dimensional and one-dimensional disordered systems with long-range interactions described by band random matrices. We investigate the convergence properties of the whole Lyapunov spectra of finite samples as a function of the bandwidth and of the sample length. Two different scaling laws are found at the maximal and minimal Lyapunov exponents. ...

In this paper, we examine the problem of the stability analysis for linear delay-differential systems. Using Lyapunov method, we present sufficient conditions for the stability of the systems in terms of linear matrix inequality (LMI) Based on the Lyapunov– Krasovskii functional techniques which can be easily solved by using YALMIP Tool box. Numerical examples are given to illustrate our results.

A novel method based on Lyapunov-Krasovskii functionals for the stability analysis of linear systems with constant is introduced. The Lyapunov-Krasovskii functionals are provided using polynomial parameters. Stability conditions are derived in the form of linear matrix inequalities. Examples show that these computationally tractable conditions can give tighter stability results than the ones in...

in this paper we consider the problem of delay-dependent robusth1 control for uncertain fuzzy systems with time-varying delay. the takagi–sugeno (t–s) fuzzy model is used to describe such systems. time-delay isassumed to have lower and upper bounds. based on the lyapunov-krasovskiifunctional method, a sufficient condition for the existence of a robust $h_{infty}$controller is obtained. the fuzz...

This paper presents an original practical criterion of global stability analysis of nonlinear polynomial systems. This criterion derived from the application of the Lyapunov direct method with a quadratic function generalizes the famous Lyapunov stability condition for linear systems. Useful mathematical transformations have allowed the formulation of the obtained conditions as an LMI (Linear M...

We provide a systematic method to validate the domain of Lyapunov functions around hyperbolic fixed points both for continuous and for discrete dynamical systems with computer assistance. We also give the construction of Lyapunov functions around periodic orbits as fixed points of Poincaré maps as well as validation examples in our talk.