Cooperative oscillatory behavior of mutually coupled dynamical systems

Pogromsky, Alexander Yu.; Nijmeijer, Henk

doi:10.1109/81.904879

Cited by 246 publications

(179 citation statements)

References 26 publications

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“…However, as was shown in (Pogromsky and Nijmeijer, 2001) the occurrence of full synchronization in large networks is significantly limited. Indeed, if all diffusive coefficients γ ij are bounded and each cell is connected with no more than N other cells, then zero is an accumulation point in the spectrum of Γ when k → ∞ (Pogromsky and Nijmeijer, 2001).…”

Section: Problem Statementmentioning

confidence: 99%

“…It has been proved in (Pogromsky and Nijmeijer, 2001) that under some additional assumptions if the lowest nonzero eigenvalue of Γ exceeds some threshold value the closed loop system (7,8) has globally asymptotically stable compact subset of the invariant set…”

Section: Problem Statementmentioning

confidence: 99%

“…Additionally, if there exists only one eigenvector associated with the zero eigenvalue of Γ then the network of the diffusively coupled systems can not be divided into two or more disconnected networks (the dimension of kerΓ is the number of disconnected networks). Networks of this kind will be referred to as diffusive cellular networks (Pogromsky and Nijmeijer, 2001). …”

Section: Problem Statementmentioning

confidence: 99%

See 2 more Smart Citations

Partial Synchronization Through Permutation Symmetry

Pogromsky

Santoboni

Nijmeijer

2002

IFAC Proceedings Volumes

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In this paper we consider the problem of the existence and stability of invariant manifolds in a network of diffusively coupled identical systems. It is shown that the existence of a symmetry in the network implies the existence of linear invariant manifolds. This correspond to so called partial synchronization, or clusterization, a phenomenon occurring when some subsystems from the network operate in a synchronous manner. Conditions guaranteeing global asymptotic stability of the partial synchronization manifolds are presented.

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Section: Problem Statementmentioning

confidence: 99%

Section: Problem Statementmentioning

confidence: 99%

Section: Problem Statementmentioning

confidence: 99%

See 1 more Smart Citation

Partial Synchronization Through Permutation Symmetry

Pogromsky

Santoboni

Nijmeijer

2002

IFAC Proceedings Volumes

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“…When studying the time-delayed network synchronization, the change of coordinates e = (R ⊗ In)X can be used [24] [22], where R is the nonsingular matrix N × N ,…”

Section: Definition 1 the System (1) Is Called Dissipative If There Ementioning

confidence: 99%

Time-Varying Delay Passivity Analysis in 4 GHz Antennas Array Design

Cauët

Huţu

Coirault

2010

Circuits Syst Signal Process

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In this paper, a new approach for synchronization of dynamical networks with time-delays is proposed. It is based on stability theory on coupled time-delayed dynamical systems. Some new criteria for the stability analysis which ensure the synchronization of the networks are analytically derived. Conditions for synchronization, in the form of a matrix inequality, are established. It uses the Lyapunov and Krasovskii stability theories. The problem of stabilization is transformed into a linear matrix inequality (LMI) which is easily solved by a numerical toolbox. In this approach, parameter uncertainties are introduced in the network model. Numerical simulations show the efficiency of the proposed synchronization analysis. A network of 4-GHz smart antenna array is used and analyzed in some details. This array provides a control of the direction of the radiation pattern.

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“…In the synchronization problem, one investigates conditions under which the state variables of all the subsystems asymptotically converge to each other, while in the formation control problem, one studies the distributed control laws which ensure that the position or the velocity of all the subsystems converge to the desired position or velocity. Passivity ( [1], [3], [12], [11]), or the weaker notion of semi-passivity ( [9], [8], [14]), has been studied in both the synchronization and formation control problems. In the context of output synchronization, the notion of incrementally passive nonlinear systems has been exploited to show that the relative output measurements in a network suffice to ensure output synchronization, i.e., the outputs of all the subsystems asymptotically converge to each other [12].…”

Section: Introductionmentioning

confidence: 99%

On the internal model principle in formation control and in output synchronization of nonlinear systems

Persis

Jayawardhana

2012

2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

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Abstract-The role of internal model principle is investigated in this paper in the context of collective synchronization and formation control problems. In the collective synchronization problem for nonlinear systems, we propose distributed control laws for passive systems which synchronize to the solution of an incrementally passive exosystem. This generalizes the result from linear systems where the existence of an internal model is required for the output synchronization of networked systems. In our second result, a distributed control law that solves a formation control problem for incrementally passive systems is proposed based also on the internal model principle.

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Cooperative oscillatory behavior of mutually coupled dynamical systems

Cited by 246 publications

References 26 publications

Partial Synchronization Through Permutation Symmetry

Partial Synchronization Through Permutation Symmetry

Time-Varying Delay Passivity Analysis in 4 GHz Antennas Array Design

On the internal model principle in formation control and in output synchronization of nonlinear systems

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