Search results for "pun"
showing 10 items of 1409 documents
Chaotic Scattering in the Gaussian Potential
1995
It is well known that general classical Hamiltonian dynamical systems have as a rule chaotic behaviour. By such a term one usually understands a sensitive dependence on initial conditions which manifests itself in the topology of phase space. For the most studied case of bounded motions this behaviour is detected, for example, by analysing the Poincare surfaces of section and by calculating Lyapunov characteristic exponents. The question then naturally arises of what are the effects of this complexity on the unbounded motions, i.e., on scattering phenomena. The signature of chaotic dynamics in these scattering regions of phase space has been the object of several papers appeared mainly in t…
Structure of equilibrium states on self-affine sets and strict monotonicity of affinity dimension
2017
A fundamental problem in the dimension theory of self-affine sets is the construction of high- dimensional measures which yield sharp lower bounds for the Hausdorff dimension of the set. A natural strategy for the construction of such high-dimensional measures is to investigate measures of maximal Lyapunov dimension; these measures can be alternatively interpreted as equilibrium states of the singular value function introduced by Falconer. Whilst the existence of these equilibrium states has been well-known for some years their structure has remained elusive, particularly in dimensions higher than two. In this article we give a complete description of the equilibrium states of the singular …
Analytic Exact Upper Bound for the Lyapunov Dimension of the Shimizu–Morioka System
2015
In applied investigations, the invariance of the Lyapunov dimension under a diffeomorphism is often used. However, in the case of irregular linearization, this fact was not strictly considered in the classical works. In the present work, the invariance of the Lyapunov dimension under diffeomorphism is demonstrated in the general case. This fact is used to obtain the analytic exact upper bound of the Lyapunov dimension of an attractor of the Shimizu–Morioka system. peerReviewed
Analysis of singular bilinear systems using Walsh functions
1991
The use of Walsh functions to analyse singular bilinear systems is investigated. It is shown that the nonlinear implicit differential system equation may be converted to a set of linear algebraic Lyapunov equations to be solved iteratively for the coefficients of the semistate x(t) in terms of the Walsh basis functions. Solution of the iterative algorithm is uniformly convergent to the exact solution of the algebraic generalised Lyapunov equation of the singular bilinear system. The present method is slightly more complicated than a similar one arising from the analysis of linear singular systems. In fact, it is a hybrid between the analyses of usual linear singular and bilinear regular sys…
Global stability of coupled Markovian switching reaction–diffusion systems on networks
2014
Abstract In this paper, we investigate the stability problem for some Markovian switching reaction–diffusion coupled systems on networks (MSRDCSNs). By using the Lyapunov function, we establish some novel stability principles for stochastic stability, asymptotically stochastic stability, globally asymptotically stochastic stability and almost surely exponential stability of the MSRDCSNs. These stability principles have a close relation to the topology property of the network. We also provide a systematic method for constructing global Lyapunov function for these MSRDCSNs by using graph theory. The new method can help analyze the dynamics of complex networks.
Sampled-Data Control of Spacecraft Rendezvous with Discontinuous Lyapunov Approach
2013
Published version of an article in the journal: Mathematical Problems in Engineering. Also available from the publisher at: http://dx.doi.org/10.1155/2013/814271 Open Access This paper investigates the sampled-data stabilization problem of spacecraft relative positional holding with improved Lyapunov function approach. The classical Clohessy-Wiltshire equation is adopted to describe the relative dynamic model. The relative position holding problem is converted into an output tracking control problem using sampling signals. A time-dependent discontinuous Lyapunov functionals approach is developed, which will lead to essentially less conservative results for the stability analysis and control…
A generalized Degn–Harrison reaction–diffusion system: Asymptotic stability and non-existence results
2021
Abstract In this paper we study the Degn–Harrison system with a generalized reaction term. Once proved the global existence and boundedness of a unique solution, we address the asymptotic behavior of the system. The conditions for the global asymptotic stability of the steady state solution are derived using the appropriate techniques based on the eigen-analysis, the Poincare–Bendixson theorem and the direct Lyapunov method. Numerical simulations are also shown to corroborate the asymptotic stability predictions. Moreover, we determine the constraints on the size of the reactor and the diffusion coefficient such that the system does not admit non-constant positive steady state solutions.
Design of unknown inputs proportional integral observers for TS fuzzy models
2014
In this paper the design of unknown inputs proportional integral observers for Takagi-Sugeno (TS) fuzzy models subject to unmeasurable decision variables is proposed. These unknown inputs affect both state and output of the system. The synthesis of these observers is based on two hypotheses that the unknown inputs are under the polynomials form with their kth derivatives zero for the first one and bounded norm for the second one, hence two approaches. The Lyapunov theory and L"2-gain technique are used to develop the stability conditions of such observers in LMIs (linear matrix inequality) formulation. A simulation example is given to validate and compare the proposed design conditions for …
FPGA Implementation Of Diffusive Realization For A Distributed Control Operator
2010
International audience; We focus on the question of real-time computation for optimal distributed filtering or control applicable to MEMS Arrays. We present an algorithm for the realization of a linear operator solution to a functional equation through its application to a Lyapunov operatorial equation associated to the heat equation in one dimension. It is based on the diffusive realization, and turns to be well suited for fined grained parallel computer architecture as Field Programmable Gate Arrays (FPGA). An effective FPGA implementation has been successfully carried out. Here, we report the main implementation steps and the final measured performances.
Input-Output Feedback Linearization Control with On-Line Inductances Estimation of Synchronous Reluctance Motors
2021
This paper proposes an adaptive input-output Feedback Linearization (FL) techniques for Synchronous Reluctance Motor (SynRM) drives, taking into consideration the iron losses. As a main original content, this work proposes a control law based on a new dynamic model of the SynRM including iron losses as well as the on-line estimation of the static inductances. The on-line estimation of the SynRM static inductances permits to inherently take into consideration the magnetic saturation phenomena occuring on both axes. The estimation law is obtained thanks to a Lyapunov-based analysis and thus the stability of the entire control system, including the estimation algorithm, is intrinsically guaran…