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Hdr Année : 2023

Contribution on the study of complex dynamical systems: applications in population dynamics

Résumé

Many systems encountered in practice result from the switching between different individual autonomous dynamics. The first contribution of this thesis concerns the stability analysis of switching infinite-dimensional systems. A collection of converse Lyapunov theorems characterising different types of uniform exponential stability of this class of systems, through the existence of non-coercive and coercive Lyapunov functionals, is given. Based on these results, several interesting control properties like the sampled data control design for semilinear switching systems, are obtained. Seeing as a particular class of infinite-dimensional systems, the class of retarded switching systems is further studied. Various stability notions like input-to-state and asymptotic stability are characterised by the existence of common Lyapunov--Krasovskii functionals with suitable conditions. The practical significance of the obtained results is shown through various derived useful theorems like a first order approximation theorem for nonlinear switching retarded systems. More elaborated properties around time-delay systems are also presented. The first property concerns the input-output linearisation problem of time-varying delay control systems with affine control; sufficient conditions guarantying the solvability of the input-output linearisation problem are given. The second property concerns the viability analysis of non-convex delay differential inclusions under state constraints. Other contributions in mathematical modelling, analysis and control in different domain of population dynamics are also presented. In particular, the observability problem of microbial dynamics in batch bioreactors and the newly developed approach in this context is presented. Another contribution concerning the modelling and optimal control of the electro-fermentation process in a batch polarised bioreactor is also given.
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Dates et versions

tel-04165090 , version 1 (18-07-2023)

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  • HAL Id : tel-04165090 , version 1

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Ihab Haidar. Contribution on the study of complex dynamical systems: applications in population dynamics. Automatic Control Engineering. CY Cergy Paris Université, 2023. ⟨tel-04165090⟩
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