Takens, Ruelle, Eckmann, Sano and Sawada launched an investigation of images of attractors of dynamical systems. Let A be a compact invariant set for a map f on Rn and let φ : Rn → Rm where n > m be a “typical” smooth map. When can we say that A and φ(A) are similar, based only on knowledge of the images in Rm of trajectories in A? For example, under what conditions on φ(A) (and the induced dyn...

this study proposes a combination of a fuzzy sliding mode controller (fsmc) with integral-proportion-derivative switching surface based superconducting magnetic energy storage (smes) and pid tuned by a multi-objective optimization algorithm to solve the load frequency control in power systems. the goal of design is to improve the dynamic response of power systems after load demand changes. in t...

Motivated by the basic problem of studying stability of nonautonomous linear systems, different definitions of spectra have been proposed over the years. We review some of these definitions, paying particular attention to how the spectra may be computed. Since the spectra are given by intervals of the real line, one would like to compute the endpoints of these intervals. As it turns out, these ...

Motivated by the work of D. Y. Kleinbock, E. Lindenstrauss, G. A. Margulis, and B. Weiss [7, 8], we explore the Diophantine properties of probability measures invariant under the Gauss map. Specifically, we prove that every such measure which has finite Lyapunov exponent is extremal, i.e. gives zero measure to the set of very well approximable numbers. We show on the other hand that there exist...

We apply the method of time-dependent rescalings which has been developed by G. Rein and the author to a model kinetic equation, to the Euler equations for a perfect polytropic gas and to a model with friction and heat transfer. We build Lyapunov functionals which are in the case of the uid models improved versions of the estimates which have been found by J.-Y. Chemin and D. Serre (see 2], 14]).

A linear system in two dimensions is studied. The coeecients are 2{periodic on three angles, j ; j = 1; 2; 3; and these angles are linear with respect to time, with incommensurable frequencies. The system has positive Lyapunov coeecients and the rotation number changes in a continuous way when some parameter moves. A lift to T 3 R 2 ; however, is only of class L p ; for any p < 2: (1) where M 2...

We consider an SIR model of disease transmission which has been formulated with delay in order to give a fixed duration of infectiousness. A Lyapunov functional that has worked for similar models does not work here. Instead, the model is shown to be a consequence of an age-of-infection model for which the same class of Lyapunov functionals has worked, resolving the global stability. In this pap...

The control of a network of signalized intersections is considered. Previous works proposed a feedback control belonging to the family of the so-called back-pressure controls that ensures provably maximum stability given pre-specified routing probabilities. However, this optimal back-pressure controller (BP*) requires routing rates and a measure of the number of vehicles queuing at a node for e...

In recent years the literature on wireless networks has been enriched by several theoretical results that have developed new mathematical frameworks for design of optimal cross-layer protocols [1]. A particularly appealing stochastic network optimization approach that yields simple distributed algorithms for dynamic scenarios is based on the use of Lyapunov drifts [2]. The Lyapunov drift based ...

In this paper, we consider the problem of flow control together with power allocation to antennas on satellite with arbitrary link states, so as to maximize the utility function while stabilizing the network. Inspired by Lyapunov optimization method, a Degree-Limited Scheduling Algorithm (DLSA) is proposed with a control parameter V, which requires no stochastic knowledge of link state. Discuss...