The transport properties of the Ando model on square lattice are studied numerically for box distribution of the diagonal disorder. The statistical properties of the Lyapunov exponents and of the conductance are discussed. It is shown that the statistics of the Lyapunov exponents agrees with the random matrix theory not only in the metallic regime, but even at the critical point. That confirms ...

Different definitions of spectra have been proposed during the years to characterize the asymptotic behavior of nonautonomous linear systems. Here, we consider the spectrum based on exponential dichotomy of Sacker and Sell and the spectrum defined in terms of upper and lower Lyapunov exponents. A main goal of ours is to understand to what extent these spectra are computable. By using an orthogo...

In some quasi-one-dimensional weakly disordered media, impurities are large and rare rather than small and dense. For an Anderson model with a low density of strong impurities, a perturbation theory in the impurity density is developed for the Lyapunov exponent and the density of states. The Lyapunov exponent grows linearly with the density. Anomalies of the Kappus-Wegner type appear for all ra...

This paper presents an adaptive nonlinear position controller with velocity constraint, capable of combining the input-output linearization technique and Lyapunov stability theory. Based on the Lyapunov stability theory, the adaptation law of the proposed controller is derived along with the verification of the overall system’s stability. Computer simulation results demonstrate that the propose...

We present a study of the transfer of satellites between elliptic Keplerian orbits using Lyapunov stability theory specific to this problem. The construction of Lyapunov functions is based on the fact that a non-degenerate Keplerian orbit is uniquely described by its angular momentum and Laplace (Runge-Lenz) vectors. We suggest a Lyapunov function, which gives a feedback controller such that th...

Pavel V. Kuptsov ∗ and Ulrich Parlitz 3 Department of Instrumentation Engineering, Saratov State Technical University, Politekhnicheskaya 77, Saratov 410054, Russia Biomedical Physics Group, Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077 Göttingen, Germany Institute for Nonlinear Dynamics, Georg–August–Universität Göttingen, Am Fassberg 17, 37077 Göttingen, German...

This paper deals with a general class of discrete 2D systems based on the Roesser model. We first discuss the existing definitions of (Lyapunov) stability in the area of multidimensional systems and provide strong incentives to adopt new definitions in order to be coherent with the ones usually adopted in the 1D case. Once this background has been carefully designed, we develop different Lyapun...

We provide general methods for explicitly constructing strict Lyapunov functions for fully nonlinear slowly time-varying systems. Our results apply to cases where the given dynamics and corresponding frozen dynamics are not necessarily exponentially stable. This complements our previous Lyapunov function constructions for rapidly time-varying dynamics. We also explicitly construct input-to-stat...