The dynamic instability of single-walled carbon nanotubes (SWCNT), double-walled carbon nanotubes (DWCNT) and triple-walled carbon nanotubes (TWCNT) embedded in an elastic medium under combined static and periodic axial loads are investigated using Floquet–Lyapunov theory. An elastic multiple-beam model is utilized where the nested slender nanotubes are coupled with each other through the van d...

Some connections between constructive real algebraic geometry and constrained optimization are exploited. We show how the problem of determining the projection of a real-algebraic variety on a certain axis is equivalent to a problem in nonlinear programming. As an application, Grr obner bases are used to deal with an optimization problem arising in the theory of local Lyapunov functions. The pr...

We present a method for the construction of Foster-Lyapunov functions to prove ergodicity of hybrid piecewise-deterministic Markov processes. Our method searches for the Lyapunov function that maximizes a measure of the rate of convergence that appears in the theory of large deviations. We provide conditions under which such a Lyapunov function is the limit of an iterative procedure. Analytical...

This paper presents a complex-valued version of the Lyapunov theory-based adaptive filtering algorithm [1]. The resulting algorithm simultaneously updates the real and imaginary parts of the complex coefficients so that the complex error can converge to zero asymptotically. The proposed scheme can be applied to random and deterministic processes because only the desired signal and input signal ...

in this paper, under the existence of system uncertainties, external disturbances, and input nonlinearity, global finite time synchronization between two identical attractors which belong to a class of second-order chaotic nonlinear gyros are achieved by considering a method of continuous smooth second-order sliding mode control (hoamsc). it is proved that the proposed controller is robust to m...

Stability plays an important role in the theory of dynamical systems and control. It characterizes the property of an unperturbed trajectory that all perturbed trajectories starting nearby stay nearby: small perturbations cause only small changes in the system behavior. The most important concept of stability has bee introduced by the Russian mathematician A. M. Lyapunov in 1892. Based on his f...

By studying the integrated density of states, we prove the existence of Lyapunov exponents and the Thouless formula for the Schrödinger operator −d2/dx2 + cos xν with 0 < ν < 1 on L2[0,∞). This yields an explicit formula for these Lyapunov exponents. By applying rank one perturbation theory, we also obtain some spectral consequences.

in this paper, global robust stability of stochastic impulsive recurrent neural networks with time-varyingdelays which are represented by the takagi-sugeno (t-s) fuzzy models is considered. a novel linear matrix inequality (lmi)-based stability criterion is obtained by using lyapunov functional theory to guarantee the asymptotic stability of uncertain fuzzy stochastic impulsive recurrent neural...