On the Coalescence of Spectral Values and its Effect on the Stability of Time-delay Systems: Application to Active Vibration Control
TLDR
For linear delay-differential equations, a question of ongoing interest is to determine conditions on the equation parameters that guarantee exponential stability of solutions as mentioned in this paper, and such an idea is presented and exploited in the control of active vibrations.About:
This article is published in Procedia IUTAM.The article was published on 2017-01-01 and is currently open access. It has received 26 citations till now. The article focuses on the topics: Exponential stability & Active vibration control.read more
Citations
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Journal ArticleDOI
Differential-Difference Equations. By Richard Bellman and Kenneth L. Cooke. Pp. xvi, 465. 1963. (Academic Press)
Journal ArticleDOI
Further remarks on the effect of multiple spectral values on the dynamics of time-delay systems. Application to the control of a mechanical system
TL;DR: In this paper, a new interesting property of linear time-delay systems was emphasized and a multiplicity induced stability criteria for reduced order systems; scalar delay-equations and a special class of second order systems.
Journal ArticleDOI
Multiplicity-induced-dominancy in parametric second-order delay differential equations: Analysis and application in control design
TL;DR: In this article, a parametric multiplicity-induced dominancy property is characterized, allowing to a delayed stabilizing design with reduced complexity, where the candidates' delays and gains result from the manifold defining the maximal multiplicity of a real spectral value, then, the dominancy is shown using the argument principle.
Journal ArticleDOI
On the Dominancy of Multiple Spectral Values for Time-delay Systems with Applications
TL;DR: In this paper, a further extension of a result on maximal multiplicity induced-dominancy for spectral values is derived for generic retarded second-order systems with a single delay in the parameter space.
References
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Book
Differential-Difference Equations
Richard Bellman,Kenneth L. Cooke +1 more
TL;DR: In this paper, the authors introduce the study of differential difference equations and discuss some of the main features of the theory, and discuss the asymptotic behavior of solutions and the problem of stability.
Journal ArticleDOI
Differential-Difference Equations. By Richard Bellman and Kenneth L. Cooke. Pp. xvi, 465. 1963. (Academic Press)
Book
Mechanical Vibrations: Theory and Application to Structural Dynamics
Michel Géradin,Daniel J. Rixen +1 more
TL;DR: In this paper, the authors present a method for the Eigenvalue Problem with Direct Time-Integration Methods (DTIM) for estimating the approximate Eigenvalues of continuous systems.
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