Counting Characteristic Roots of Linear Delay Differential Equations. Part II: from Argument Principle to Rightmost Root Assignment Methods - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Book Sections Year : 2022

Counting Characteristic Roots of Linear Delay Differential Equations. Part II: from Argument Principle to Rightmost Root Assignment Methods

Abstract

This chapter briefly presents some "user-friendly" methods and techniques (frequency-domain approaches) for the analysis and control of linear dynamical systems in presence of delays. The presentation is as simple as possible, focusing more on the main intuitive (algebraic, geometric) ideas to develop theoretical results, and their potential use in practical applications. To fix better the ideas, scalar and second-order examples are largely discussed. Next, a particular attention will be paid to the existing links between the maximal allowable multiplicity of the characteristic roots and the spectral abscissa of the dynamical system. The underlying property-multiplicity induced dominancy-will be particularly useful in constructing low-complexity controllers by partial pole placement. Such an idea is particularly exploited in vibration control.
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Dates and versions

hal-03634874 , version 1 (08-04-2022)

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Silviu-Iulian Niculescu, Islam Boussaada. Counting Characteristic Roots of Linear Delay Differential Equations. Part II: from Argument Principle to Rightmost Root Assignment Methods. CONTROLLING DELAYED DYNAMICS: ADVANCES IN THEORY, METHODS AND APPLICATIONS, 2022, ⟨10.1007/978-3-031-01129-0_6⟩. ⟨hal-03634874⟩
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