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Canards et râteaux

Augustin Fruchard (1992)

Annales de l'institut Fourier

On étudie le phénomène de retard à la bifurcation dans des systèmes dynamiques discrets du plan. La distinction d’une courbe invariante par le système permet de ramener l’étude de ce phénomène à l’étude d’un objet. On démontre la présence du retard dans les systèmes analytiques oscillants. On fait état d’un nouveau phénomène découvert expérimentalement qui apparaît dans les systèmes non inversibles: la courbe invariante présente une succession de pôles exponentiellement étroits. On démontre la présence...

Canonical forms of singular 1D and 2D linear systems

Tadeusz Kaczorek (2003)

International Journal of Applied Mathematics and Computer Science

The paper consists of two parts. In the first part, new canonical forms are defined for singular 1D linear systems and a procedure to determine nonsingular matrices transforming matrices of singular systems to their canonical forms is derived. In the second part new canonical forms of matrices of the singular 2D Roesser model are defined and a procedure for determining realisations in canonical forms for a given 2D transfer function is presented. Necessary and sufficient conditions for the existence...

Compact Global Chaotic Attractors of Discrete Control Systems

David Cheban (2014)

Nonautonomous Dynamical Systems

The paper is dedicated to the study of the problem of existence of compact global chaotic attractors of discrete control systems and to the description of its structure. We consider so called switched systems with discrete time xn+1 = fν(n)(xn), where ν : ℤ+ ⃗ {1,2,...,m}. If m ≥ 2 we give sufficient conditions (the family M := {f1,f2,...,fm} of functions is contracting in the extended sense) for the existence of a compact global chaotic attractor. We study this problem in the framework of non-autonomous...

Controllability and observability of linear discrete-time fractional-order systems

Said Guermah, Said Djennoune, Maamar Bettayeb (2008)

International Journal of Applied Mathematics and Computer Science

In this paper we extend some basic results on the controllability and observability of linear discrete-time fractional-order systems. For both of these fundamental structural properties we establish some new concepts inherent to fractional-order systems and we develop new analytical methods for checking these properties. Numerical examples are presented to illustrate the theoretical results.

Controllability and reconstructability of a system described by the N-D Roesser model

Jerzy Kurek (2003)

International Journal of Applied Mathematics and Computer Science

The controllability and reconstructability (global) of the system described by a digital N-D Roesser model are defined. Then, necessary and sufficient conditions for system controllability and reconstructability are given. The conditions constitute a generalization of the corresponding conditions for 1-D systems.

Controllability of nonlinear discrete systems

Jerzy Klamka (2002)

International Journal of Applied Mathematics and Computer Science

Local constrained controllability problems for nonlinear finite-dimensional discrete 1-D and 2-D control systems with constant coefficients are formulated and discussed. Using some mapping theorems taken from nonlinear functional analysis and linear approximation methods, sufficient conditions for constrained controllability in bounded domains are derived and proved. The paper extends the controllability conditions with unconstrained controls given in the literature to cover both 1-D and 2-D nonlinear...

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