We present a formula for a stabilizing feedback law under the assumption that a piecewise smooth controlLyapunov function exists. The resulting feedback is continuous at the origin and smooth everywhere except on a hypersurface of codimension 1. We provide an explicit and “universal” formula. Finally, we mention a general result connecting asymptotic controllability and the existence of control...

The interest in memristors has risen due to their possible application both as memory units and as computational devices in combination with CMOS. This is in part due to their nonlinear dynamics and a strong dependence on the circuit topology. We provide evidence that also purely memristive circuits can be employed for computational purposes. We show that a Lyapunov function, polynomial in the ...

We consider a Fokker-Planck equation in a general domain in R with Lploc drift term and W 1,p loc diffusion term for any p > n. By deriving an integral identity, we give several measure estimates of regular stationary measures in an exterior domain with respect to diffusion and Lyapunov-like or anti-Lyapunov-like functions. These estimates will be useful to problems such as the existence and no...

The notion of non-uniform Robust Global Asymptotic Stability (RGAS) presented in this paper generalizes the notion of non-uniform in time RGAS for finiteor infinite-dimensional discrete-time systems. Lyapunov characterizations for this stability notion are provided. The results are applied to finitedimensional discrete-time systems obtained by time discretization of continuous-time systems by t...

We report a study of dynamical intramolecular energy transfer in a realistic polyatomic molecular model system of cyclobutanone (C 4 H 6 O). It appears that for this two degree-of-freedom model system, Lyapunov relaxation does yield the same time scale as intramolecular energy exchange .

We prove several theorems that lend support for Greene's criterion for existence or not of invariant circles in twist maps. In particular, we show that some of the implications of the criterion are correct when the Aubry-Mather sets are smooth invariant circles or uniformly hyperbolic. We also suggest a simple modiication that can work in the case that the Aubry-Mather sets have non-zero Lyapun...

In this paper, we propose an epidemic model with age-dependence vaccination, latency and relapse. We derive the positivity and boundedness of solutions and find the basic reproduction number. Asymptotic smoothness, the existence of global compact attractor and uniform persistence of the model are investigated. By constructing Lyapunov functionals, we establish global stability of the equilibria...

*Correspondence: [email protected] 1Department of Mathematics, Xinjiang Institute of Engineering, Urumqi, Xinjiang 830091, P.R. China Full list of author information is available at the end of the article Abstract In this paper, a diffusive and delayed virus dynamics model with Crowley-Martin incidence function and CTL immune response is investigated. By constructing the Lyapunov functionals...