The paper deals with the problem of estimation of the topological entropy for discrete-time nonlinear systems via the second (direct) Lyapunov method. The main result of the paper is illustrated by examples concerning the Hénon system and forced bouncing ball oscillator. An application to the observability problem via digital channels with limited data rate is discussed and the simulation resul...

This paper presents an implementation of stable direct adaptive control on nonlinear systems using lyapunov function with fuzzy approach. Stable direct adaptive control law consists of an ideal control, and a sliding mode control. Sliding mode controller is used to ensure the stability of Lyapunov function. Stability of direct adaptive control law is tested on two nonlinear systems. Non linear ...

We study switched nonlinear differential algebraic equations (DAEs) with respect to existence and nature of solutions as well as stability. We utilize piecewise-smooth distributions introduced in earlier work for linear switched DAEs to establish a solution framework for switched nonlinear DAEs. In particular, we allow induced jumps in the solutions. To study stability, we first generalize Lyap...

Lyapunov’s direct method. Two matrix equations have been derived: matrix polynomial equation and continuous (discrete) Lyapunov matrix equation. Also, modifications of the existing sufficient conditions of convergence of Traub and Bernoilli algorithms for computing the dominant solvent of the matrix polynomial equation are derived. These results have been extended to large scale systems as well...

This paper suggests a new stability analysis theorem dedicated to a class of fuzzy logic control systems. The fuzzy logic control systems consist of nonlinear Single Input-Single Output (SISO) discrete-time processes controlled by Takagi-Sugeno fuzzy logic controllers. The stability analysis is conducted on the basis of Lyapunov’s direct method with quadratic Lyapunov function candidates. The t...

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...

This paper studies the global synchronization for undirect and direct coupled networks with delay by employing Lyapunov functional method and Kronecker product technique. A novel pinning scheme is proposed and some sufficient conditions are given to ensure the global synchronization of coupled networks. Finally, an example is given to show the effectiveness of the proposed pinning scheme.

In this work, an attempt is made to detect the chaotic nature of smooth monthly sunspot (SSN) time series using various nonlinear analysis techniques to quantify the uncertainty involved. Different nonlinear dynamic methods, with varying levels of complexity, are employed such as average mutual information and embedding dimension method to construct a phase space. The correlation dimension meth...

4 Lyapunov Exponents 5 4.1 Definition and basic properties . . . . 6 4.2 Constraints on the Lyapunov exponents 7 4.3 Calculating the largest Lyapunov exponent method 1 . . . . . . . . . . . 7 4.4 Calculating the largest Lyapunov exponent method 2 . . . . . . . . . . . 8 4.4.1 Maps . . . . . . . . . . . . . . 8 4.4.2 Continuous systems . . . . . . 8 4.5 Calculating the other Lyapunov exponents ....

Urban industrial water system parameter fluctuation producing uncertainty may not occur in a control input channel, can be applied mismatching uncertain system to describe. Based on Lyapunov direct method and linear matrix inequality, design the urban industrial water mismatching uncertain system feedback stabilization robust control scheme. Avoid the defects that the feedback stabilization con...