Catherine Bonnet

Brief Analysis of fractional delay systems of retarded and neutral type

This paper analyses several properties linked to the robust control of fractional differential systems with delays. The BIBO stability of both retarded and neutral fractional delay systems is related to the location of their poles. In the particular case of retarded systems, we give some properties of the poles of the system and the singular values of its Hankel operator.

Coprime factorizations and stability of fractional differential systems

We give a frequency-domain approach to stabilization for a large class of systems with transfer functions involving fractional powers of s. A necessary and sufficient criterion for BIBO stability is given, and it is shown how to construct coprime factorizations and associated Bezout factors in order to parametrize all stabilizing controllers of these systems.

H∞ and BIBO stabilization of delay systems of neutral type

Frequency-domain tests for the H∞ and BIBO stability of large classes of delay systems of neutral type are derived. The results are applied to discuss the stabilizability of such systems by finite-dimensional controllers.

PID controller design for fractional-order systems with time delays

a b s t r a c t Classical proper PID controllers are designed for linear time invariant plants whose transfer functions are rational functions of s α , where 0 < α < 1, and s is the Laplace transform variable. Effect of input-output time delay on the range of allowable controller parameters is investigated. The allowable PID controller parameters are determined from a small gain type of argument used earlier for finite dimensional plants.

A numerical method for stability windows and unstable root-locus calculation for linear fractional time-delay systems

This paper aims to provide a numerical algorithm able to locate all unstable poles, and therefore the characterization of the stability as a function of the delay, for a class of linear fractional-order neutral systems with multiple commensurate delays. We start by giving the asymptotic position of the chains of poles and the conditions for their stability for a small delay. When these conditions are met, the root continuity argument and some simple substitutions allow us to determine the locations where some roots cross the imaginary axis, providing therefore the complete characterization of the stability windows. The same method can be extended to provide the position of all unstable poles as a function of the delay.

Stability of Neutral Systems with Commensurate Delays and Poles Asymptotic to the Imaginary Axis

This paper addresses the

Stability analysis of systems with distributed delays and application to hematopoietic cell maturation dynamics

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Bezout factors and L/sup 1/-optimal controllers for delay systems using a two-parameter compensator scheme

-stability analysis of neutral time-delay systems with multiple commensurate delays, including those with poles asymptotic to the imaginary axis. The location of asymptotic poles is completely described, and easy-to-check necessary and sufficient conditions of

A new model of cell dynamics in Acute Myeloid Leukemia involving distributed delays

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A numerical method to find stability windows and unstable poles for linear neutral time-delay systems

-stability are derived. Robustness relative to a change in the delay or the parameters is discussed. Moreover,