A Frequency-Sweeping Framework for Stability Analysis of Time-Delay Systems

Li, Xuguang; Niculescu, Silviu–Iulian; Çela, Arben; Zhang, Lu

doi:10.1109/tac.2016.2633533

Cited by 48 publications

(35 citation statements)

References 21 publications

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“…Hence, as discussed by [24], it is possible to characterize the root locus of f by its branches. In fact, the equation f (s, τ ) = 0 defines a solution curve C ∈ C 2 which is composed by the finite union of r-branches s j τ 1/mj ; each of these branches can be expressed as a Puiseux series: (15) s jσ (τ ) = c jσ τ…”

Section: Splitting Propertiesmentioning

confidence: 99%

“…Their results allow computations in an efficient way. Finally, more recently, in [15], the asymptotic behavior analysis of critical solutions with respect to a infinitely many critical delays (including the case of one delay) has been considered where, in particular, the authors solve the general invariance property treated under some appropriate constraints in [13].…”

mentioning

confidence: 99%

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Weierstrass Approach to Asymptotic Behavior Characterization of Critical Imaginary Roots for Retarded Differential Equations

Martínez-González

Méndez-Barrios²,

Niculescu

et al. 2019

SIAM J. Control Optim.

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This paper focuses on the analysis of the behavior of characteristic roots of timedelay systems, when the delay is subject to small parameter variations. The analysis is performed by means of the Weierstrass polynomial. More specifically, such a polynomial is employed to study the stability behavior of the characteristic roots with respect to small variations on the delay parameter. Analytic and splitting properties of the Puiseux series expansions of critical roots are characterized by allowing a full description of the cases that can be encountered. Several numerical examples encountered in the control literature are considered to illustrate the effectiveness of the proposed approach.

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Section: Splitting Propertiesmentioning

confidence: 99%

mentioning

confidence: 99%

Weierstrass Approach to Asymptotic Behavior Characterization of Critical Imaginary Roots for Retarded Differential Equations

Martínez-González

Méndez-Barrios²,

Niculescu

et al. 2019

SIAM J. Control Optim.

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show abstract

“…We now adopt some useful notations introduced in [18], with which we can describe the asymptotic behaviour of a CIR (CZR) from the stability perspective. Suppose

()(, x, y)

is a critical pair with

y > 0

, we use

Δ N U_{x} ()(, y)

to denote the number change of unstable roots caused by the variation of the CIR (CZR)

λ = x

as the delay

τ

increases from

y - ε

y + ε

, i.e.…”

Section: Preliminaries and Prerequisitesmentioning

confidence: 99%

“…Recently, a new frequency‐sweeping approach was proposed in [18] for a point‐wise delay system, to overcome the peculiarity that a CIR has infinitely many CDs. With this approach, a crucial property, called the invariance property , was confirmed: The asymptotic behaviour of a CIR is invariant w.r.t.…”

Section: Preliminaries and Prerequisitesmentioning

confidence: 99%

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Stability analysis for a class of distributed delay systems with constant coefficients by using a frequency‐sweeping approach

Zhang

Mao

et al. 2019

IET Control Theory & Applications

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Theoretical and Experimental Research on Active Suspension System with Time‐Delay Control

Wu,

Ren,

et al. 2023

Advcd Theory and Sims

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Time‐delay significantly impacts the control system's performance and even leads to the unexpected instability of the control system. This paper aims at the adverse effect of time‐delay on the control effect and stability of the active suspension system. This paper proposes to suppress vehicle body vibration by applying time‐delay displacement feedback. In this paper, the time‐delay control characteristics of the system are studied by combining theory with experiment. This paper first establishes the suspension system's dynamic Equation with time‐delay. Then, the frequency domain sweep method is used to analyze the stability of the control system. Finally, the time‐delay simulation model is established, and the single‐frequency excitation is used as the external excitation to compare with passive and backstepping control. The simulation results verify the superiority of the time‐delay control under external excitation. In this paper, through the 1/4 model bench test of the active suspension system, the simulation results and the test results under the same working conditions are compared, and it is found that the two have good consistency. The results show that the research is credible and can provide a reference for the actual design and application of active vehicle suspension controllers.

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A Frequency-Sweeping Framework for Stability Analysis of Time-Delay Systems

Cited by 48 publications

References 21 publications

Weierstrass Approach to Asymptotic Behavior Characterization of Critical Imaginary Roots for Retarded Differential Equations

Weierstrass Approach to Asymptotic Behavior Characterization of Critical Imaginary Roots for Retarded Differential Equations

Stability analysis for a class of distributed delay systems with constant coefficients by using a frequency‐sweeping approach

Theoretical and Experimental Research on Active Suspension System with Time‐Delay Control

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