Frequency Methods in Oscillation Theory

Leonov, Gennadij A.; Burkin, I. M.; Shepeljavyi, Alexander I.

doi:10.1007/978-94-009-0193-3

Cited by 158 publications

(119 citation statements)

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“…Corresponding modifications of the classic stability criteria for the rigorous analytical analysis of nonlinear PLL-based model in the cylindrical phase space had been well developed in 197x-199x in [27]- [29]. See also some recent works on nonlinear methods for the analysis of PLL-based models [17], [30]- [36].…”

Section: Discussionmentioning

confidence: 99%

A short survey on nonlinear models of the classic Costas loop: Rigorous derivation and limitations of the classic analysis

Best¹,

Kuznetsov

Леонов

et al. 2015

2015 American Control Conference (ACC)

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Abstract-Rigorous nonlinear analysis of the physical model of Costas loop -a classic phase-locked loop (PLL) based circuit for carrier recovery, is a challenging task. Thus for its analysis, simplified mathematical models and numerical simulation are widely used. In this work a short survey on nonlinear models of the BPSK Costas loop, used for pre-design and post-design analysis, is presented. Their rigorous derivation and limitations of classic analysis are discussed. It is shown that the use of simplified mathematical models, and the application of non rigorous methods of analysis (e.g., simulation and linearization) may lead to wrong conclusions concerning the performance of the Costas loop physical model.

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Section: Discussionmentioning

confidence: 99%

A short survey on nonlinear models of the classic Costas loop: Rigorous derivation and limitations of the classic analysis

Best¹,

Kuznetsov

Леонов

et al. 2015

2015 American Control Conference (ACC)

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“…In a few years later he introduced (1973) a new definition of self-sustained oscillations (or auto-oscillation) and proposed conditions of this type of oscillations existence for Lurie systems (Yakubovich, 1975;Yakubovich and Tomberg, 1989) (in work (Yakubovich, 1975) conditions of oscillatority for systems with discontinuous at the origin nonlinearity were presented). This type of oscillatority later received the name of Prof. Yakubovich (Leonov, et al, 1995). Recently those conditions of the oscillatority were extended to generic nonlinear systems decomposed in nonlinear dynamical subsystem closed by static nonlinear output feedback (Efimov and Fradkov, 2004;2007).…”

Section: Introductionmentioning

confidence: 99%

On PERIODICAL OSCILLATIONS of LURIE SYSTEMS with DISCONTINUOUS NONLINEARITY

Efimov

2008

IFAC Proceedings Volumes

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“…Item (ii) is a uniform global attractivity property of every solution, as the constant T is the same for all maximal solutions φ 1 and φ 2 with δ(φ 1 (0, 0), φ 2 (0, 0)) < r, given ε, r > 0. It can be noted that the time mismatch t − t ′ of the solutions in Definition 3 reminds of Zhukovsky stability for continuous-time systems, see e.g., Chapter 8.4 in [10]. If δ is the Euclidean distance, this small time mismatch t−t ′ does not allow for the 'peaking phenomenon' of the error δ(φ 1 (t, j), φ 2 (t, j ′ )) to occur as described in e.g., [2], [6], [9], [13].…”

Section: Flow Incremental Asymptotic Stabilitymentioning

confidence: 99%

Definitions of incremental stability for hybrid systems

Biemond

Heemels

Wouw

2015

2015 54th IEEE Conference on Decision and Control (CDC)

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Abstract-The analysis of incremental stability properties typically involves measuring the distance between any pair of solutions of a given dynamical system, corresponding to different initial conditions, at the same time instant. This approach is not directly applicable for hybrid systems in general. Indeed, hybrid systems generate solutions that are defined with respect to hybrid times, which consist of both the continuous time elapsed and the discrete time, that is the number of jumps the solution has experienced. Two solutions of a hybrid system do not a priori have the same time domain, and we may therefore not be able to compare them at the same hybrid time instant. To overcome this issue, we invoke graphical closeness concepts. We present definitions for incremental stability depending on whether incremental asymptotic stability properties hold with respect to the hybrid time, the continuous time, or the discrete time, respectively. Examples are provided throughout the paper to illustrate these definitions, and the relations between these three incremental stability notions are investigated. The definitions are shown to be consistent with those available in the literature for continuous-time and discrete-time systems.

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Frequency Methods in Oscillation Theory

Cited by 158 publications

References 0 publications

A short survey on nonlinear models of the classic Costas loop: Rigorous derivation and limitations of the classic analysis

A short survey on nonlinear models of the classic Costas loop: Rigorous derivation and limitations of the classic analysis

On PERIODICAL OSCILLATIONS of LURIE SYSTEMS with DISCONTINUOUS NONLINEARITY

Definitions of incremental stability for hybrid systems

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