⎯By employing the Lyapunov stability theory and linear matrix inequality (LMI) technique, delaydependent stability criterion is derived to ensure the exponential stability of bi-directional associative memory (BAM) neural networks with time-varying delays. The proposed condition can be checked easily by LMI control toolbox in Matlab. A numerical example is given to demonstrate the effectiveness...

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...

In this contribution we report on a transition to high-dimensional chaos through three-frequency quasiperiodic behavior. The resulting chaotic attractor has a one positive and two null Lyapunov exponents. The transition occurs at the point at which two symmetry related threedimensional tori merge in a crisis-like bifurcation. The route can be summarized as: 2D torus → 3D torus→ high-dimensional...

First, this paper introduces a seven-term novel 3-D chaotic system and discusses its qualitative properties. The proposed system is a seven-term novel polynomial chaotic system with three quadratic nonlinearities. The Lyapunov exponents of the novel chaotic system are obtained as L1 = 3.3226, L2 = 0 and L3 = –30.3406. The maximal Lyapunov exponent (MLE) for the novel chaotic system is obtained ...

This survey addresses stability analysis for stochastic hybrid systems (SHS), which are dynamical systems that combine continuous change and instantaneous change and that also include random effects. We reemphasize the common features found in most of the models that have appeared in the literature, which include stochastic switched systems, Markov jump systems, impulsive stochastic systems, sw...

We consider nonlinear systems dx=dt = f(x(t)) where Df(x(t)) is known to lie in the convex hull of L matrices A1, : : : , AL 2 R n . For such systems, quadratic Lyapunov functions can be determined using convex programming techniques [1]. This paper describes an algorithm that either nds a quadratic Lyapunov function or terminates with a proof that no quadratic Lyapunov function exists. The alg...

The problem is posed to develop Lyapunov theory for diierential systems described by high-order diierential algebraic equations. The questions are how to verify positivity along solutions of functionals of the system variables, to compute their derivative along solutions, and conclude (asymptotic) stability from there.

In this paper we will extend the input-to-state stability (ISS) framework introduced by Sontag to continuous-time discontinuous dynamical systems adopting Filippov’s solution concept and using non-smooth ISS Lyapunov functions. The main motivation for investigating non-smooth ISS Lyapunov functions is the recent focus on “multiple Lyapunov functions” for which feasible computational schemes are...

We demonstrate that discrete Lyapunov exponents are isomorphic to numeric overflows of the capacity of an arbitrary noiseless and memoryless channel in a Shannon communication model with feedback. The isomorphism allows the understanding of Lyapunov exponents in terms of Information Theory, rather than the traditional definitions in chaos theory. The result also implies alternative approaches t...

In this paper we will extend the input-to-state stability (ISS) framework introduced by Sontag to continuous-time discontinuous dynamical systems adopting Filippov’s solution concept and using non-smooth ISS Lyapunov functions. The main motivation for investigating non-smooth ISS Lyapunov functions is the recent focus on “multiple Lyapunov functions” for which feasible computational schemes are...