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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...

Canonical input-output representation of linear multivariable stochastic systems and joint optimal parameter and state estimation.

G. Salut, J. Aguilar-Martín, S. Lefevre (1979)

Stochastica

In this paper a complete presentation is given of a new canonical representation of multi-input, multi-output linear stochastic systems. Its equivalence with operator form directly linked with ARMA processes as well as with classical state space representation is given, and a transfer matrix interpretation is developed in an example. The importance of the new representation is mainly in the fact that in the joint state and parameters estimation problem, all unknown parameters appear linearly when...

Chaos synchronization of TSUCS unified chaotic system, a modified function projective control method

Hamed Tirandaz (2018)

Kybernetika

The synchronization problem of the three-scroll unified chaotic system (TSUCS) is studied in this paper. A modified function projective synchronization (MFPS) method is developed to achieve this goal. Furthermore, the only parameter of the TSUCS unified chaotic system is considered unknown and estimated with an appropriate parameter estimation law. MFPS method is investigated for both identical and non-identical chaotic systems. Lyapunov stability theorem is utilized to verify the proposed feedback...

Chaotic behavior and modified function projective synchronization of a simple system with one stable equilibrium

Zhouchao Wei, Zhen Wang (2013)

Kybernetika

By introducing a feedback control to a proposed Sprott E system, an extremely complex chaotic attractor with only one stable equilibrium is derived. The system evolves into periodic and chaotic behaviors by detailed numerical as well as theoretical analysis. Analysis results show that chaos also can be generated via a period-doubling bifurcation when the system has one and only one stable equilibrium. Based on Lyapunov stability theory, the adaptive control law and the parameter update law are derived...

Characterization of generic properties of linear structured systems for efficient computations

Christian Commault, Jean-Michel Dion, Jacob W. van der Woude (2002)

Kybernetika

In this paper we investigate some of the computational aspects of generic properties of linear structured systems. In such systems only the zero/nonzero pattern of the system matrices is assumed to be known. For structured systems a number of characterizations of so-called generic properties have been obtained in the literature. The characterizations often have been presented by means of the graph associated to a linear structured system and are then expressed in terms of the maximal or minimal...

Circle criterion and boundary control systems in factor form: input-output approach

Piotr Grabowski, Frank Callier (2001)

International Journal of Applied Mathematics and Computer Science

A circle criterion is obtained for a SISO Lur’e feedback control system consist- ing of a nonlinear static sector-type controller and a linear boundary control system in factor form on an infinite-dimensional Hilbert state space H previ- ously introduced by the authors (Grabowski and Callier, 1999). It is assumed for the latter that (a) the observation functional is infinite-time admissible, (b) the factor control vector satisfies a compatibility condition, and (c) the trans- fer function belongs...

Closed-loop structure of decouplable linear multivariable systems

Javier Ruiz, Jorge Luis Orozco, Ofelia Begovich (2005)

Kybernetika

Considering a controllable, square, linear multivariable system, which is decouplable by static state feedback, we completely characterize in this paper the structure of the decoupled closed-loop system. The family of all attainable transfer function matrices for the decoupled closed-loop system is characterized, which also completely establishes all possible combinations of attainable finite pole and zero structures. The set of assignable poles as well as the set of fixed decoupling poles are determined,...

Colored decision process Petri nets: modeling, analysis and stability

Julio Clempner (2005)

International Journal of Applied Mathematics and Computer Science

In this paper we introduce a new modeling paradigm for developing a decision process representation called the Colored Decision Process Petri Net (CDPPN). It extends the Colored Petri Net (CPN) theoretic approach including Markov decision processes. CPNs are used for process representation taking advantage of the formal semantic and the graphical display. A Markov decision process is utilized as a tool for trajectory planning via a utility function. The main point of the CDPPN is its ability to...

Combining odometry and visual loop-closure detection for consistent topo-metrical mapping

S. Bazeille, D. Filliat (2010)

RAIRO - Operations Research - Recherche Opérationnelle

We address the problem of simultaneous localization and mapping (SLAM) by combining visual loop-closure detection with metrical information given by a robot odometry. The proposed algorithm extends a purely appearance-based loop-closure detection method based on bags of visual words [A. Angeli, D. Filliat, S. Doncieux and J.-A. Meyer, IEEE Transactions On Robotics, Special Issue on Visual SLAM 24 (2008) 1027–1037], which is able to detect when the robot has returned back to a previously visited...

Combining Odometry and Visual Loop-Closure Detection for Consistent Topo-Metrical Mapping

S. Bazeille, D. Filliat (2011)

RAIRO - Operations Research

We address the problem of simultaneous localization and mapping (SLAM) by combining visual loop-closure detection with metrical information given by a robot odometry. The proposed algorithm extends a purely appearance-based loop-closure detection method based on bags of visual words [A. Angeli, D. Filliat, S. Doncieux and J.-A. Meyer, IEEE Transactions On Robotics, Special Issue on Visual SLAM24 (2008) 1027–1037], which is able to detect when the robot has returned back to a previously visited...

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...

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