Entrainment to subharmonic trajectories in oscillatory discrete-time systems

Katz, Rami; Margaliot, Michael; Fridman, Emilia

doi:10.1016/j.automatica.2020.108919

Cited by 17 publications

(11 citation statements)

References 35 publications

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“…The final section concludes. In passing we note that our results are part of a growing body of research on the applications of sign-regularity (and, in particular, total positivity) to dynamical systems [1], [4], [17], [20], [28], [30].…”

Section: Introductionmentioning

confidence: 99%

Discrete-Time $k$-Positive Linear Systems

Alseidi

Margaliot

Garloff

2021

IEEE Trans. Automat. Contr.

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Positive systems play an important role in systems and control theory and have found many applications in multi-agent systems, neural networks, systems biology, and more. Positive systems map the nonnegative orthant to itself (and also the nonpositive orthant to itself). In other words, they map the set of vectors with zero sign variations to itself. In this note, discrete-time linear systems that map the set of vectors with up to k − 1 sign variations to itself are introduced. For the special case k = 1 these reduce to discrete-time positive linear systems. Properties of these systems are analyzed using tools from the theory of sign-regular matrices. In particular, it is shown that almost every solution of such systems converges to the set of vectors with up to k − 1 sign variations. Also, the operation of such systems on k-dimensional parallelotopes are studied.

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Section: Introductionmentioning

confidence: 99%

Discrete-Time $k$-Positive Linear Systems

Alseidi

Margaliot

Garloff

2021

IEEE Trans. Automat. Contr.

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“…For more details, see also [9]. For more recent applications of these compounds in systems and control theory, see [18], [19], [20], [21].…”

Section: Preliminariesmentioning

confidence: 99%

“…By Prop. 4, the system can be decomposed as the serial connection of two subsystems by defining ỹ1 := Ṽ T x z and ỹ2 := Ũ T x z , that is, ỹ1 = V T x z and ỹ2 := U T x. Computing the dynamics of yields (19).…”

Section: Combining This Variational Equation With Conditionmentioning

confidence: 99%

Serial interconnections of 1-contracting and 2-contracting systems

Ofir¹,

Margaliot²,

Levron³

et al. 2021

Preprint

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The flow of contracting systems contracts 1dimensional polygons (i.e. lines) at an exponential rate. One reason for the usefulness of contracting systems is that many interconnections of contracting sub-systems yield an overall contracting system. A recent generalization of contracting systems is called k-contracting systems, where k ∈ {1, . . . , n}.The flow of such systems contracts k-dimensional polygons at an exponential rate, and in particular they reduce to contracting systems when k = 1. Here, we analyze serial interconnections of 1-contracting and 2-contracting systems. We provide conditions guaranteeing that such interconnections have a well-ordered asymptotic behaviour, and demonstrate the theoretical results using several examples.

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“…For more details, see also [19]. For more recent applications of these compounds in systems and control theory, see [24], [25], [14], [26] and the tutorial paper [23].…”

Section: Preliminariesmentioning

confidence: 99%

A sufficient condition for $k$-contraction of the series connection of two systems

Ofir,

Margaliot,

Levron

et al. 2021

Preprint

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The flow of contracting systems contracts 1-dimensional parallelotopes, i.e., line segments, at an exponential rate. One reason for the usefulness of contracting systems is that many interconnections of contracting sub-systems yield an overall contracting system.A generalization of contracting systems is k-contracting systems, where k ∈ {1, . . . , n}. The flow of such systems contracts the volume of k-dimensional parallelotopes at an exponential rate, and in particular they reduce to contracting systems when k = 1. It was shown by Muldowney and Li that time-invariant 2-contracting systems have a well-ordered asymptotic behaviour: all bounded trajectories converge to the set of equilibria.Here, we derive a sufficient condition guaranteeing that the system obtained from the series interconnection of two sub-systems is k-contracting. This is based on a new formula for the kth multiplicative and additive compounds of a block-diagonal matrix, which may be of independent interest. As an application, we find conditions guaranteeing that 2-contracting systems with an exponentially decaying input retain the well-ordered behaviour of time-invariant 2-contracting systems.

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Entrainment to subharmonic trajectories in oscillatory discrete-time systems

Cited by 17 publications

References 35 publications

Discrete-Time $k$-Positive Linear Systems

Discrete-Time $k$-Positive Linear Systems

Serial interconnections of 1-contracting and 2-contracting systems

A sufficient condition for $k$-contraction of the series connection of two systems

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