Download Robust Control and Observation of Linear Parameter Varying by Corentin Briat PDF

By Corentin Briat

This ebook offers an creation to the research and keep an eye on of Linear Parameter-Varying platforms and Time-Delay platforms and their interactions. the aim is to provide the readers a few primary theoretical heritage on those issues and to offer extra insights at the attainable functions of those theories. This self-contained monograph is written in an obtainable method for readers starting from undergraduate/PhD scholars to engineers and researchers prepared to understand extra in regards to the fields of time-delay platforms, parameter-varying platforms, strong research, powerful keep watch over, gain-scheduling recommendations within the LPV style and LMI dependent methods. the single necessities are simple wisdom in linear algebra, traditional differential equations and (linear) dynamical platforms. lots of the effects are proved except the evidence is simply too complicated or now not important for an exceptional realizing of the implications. within the latter instances, appropriate references are systematically supplied. the 1st half pertains at the illustration, research and keep an eye on of LPV platforms besides a reminder on strong research and regulate recommendations. the second one half is worried with the illustration and research of time-delay structures utilizing a number of time-domain recommendations. The 3rd and final half is dedicated to the illustration, research, commentary, filtering and keep watch over of LPV time-delay structures. The e-book additionally provides many very important easy and complex effects at the manipulation of LMIs.

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Additional info for Robust Control and Observation of Linear Parameter Varying Time-Delay Systems

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2002]. 2 Contributions Les contributions apport´ees dans cette th`ese peuvent ˆetre class´ee en deux parties: les contributions m´ ethodologiques qui sont relatives `a la technique d’approche et la vision des probl`emes abord´es; les contributions th´ eoriques repr´esent´ees par l’am´elioration des r´esultats existants, le d´eveloppement de nouveaux r´esultats et id´ees. 1 Contributions M´ ethodologiques La contribution m´ethodologique est issue d’une remarque globale faite sur beaucoup de papiers de journaux et de conf´erences.

L’´evolution des erreurs d’observations u il est possible de voir que les erreurs convergent bien vers 0. 8. La perturbation en ´echelon d’amplitude 10 est appliqu´ee a ` t = 15s et la trajectoire des param`etres est sinuso¨ıdale ρ(t) = sin(t). 2 Filtrage L’objectif du filtrage est proche de celui de l’observation mais demeure un peu diff´erent. L’objectif est de rapprocher la sortie du filtre de celle du syst`eme le plus possible, au sens d’une certaine norme. 3. 20) Les matrices du filtre sont choisies de sorte que: 1.

L’in´egalit´e ||e||L2 ≤ γ||w||L2 est satisfaite pour un γ > 0 minimal. 15) rank      0 C     0 C  CA(ρ) CAh (ρ)  CA(ρ) CAh (ρ) T A(ρ) T Ah (ρ) pour tout ρ ∈ Uρ . 1. 3. APPLICATION A avec la matrice de plein rang colonne T¯ telle que mani`ere suivante:    ∆0 =    0 0 I 0 0 0 0 0 0 I        ∆h =      0 0 0 I 0 T T¯ 0 0 0 0 I 9 . Les matrices ∆i sont d´efinies de la        ∆H =      0 0 0 0 I       Le r´esultat suivant donne une condition suffisante sur l’existence d’un observateur optimal au sens de la minimisation de la norme L2 induite du transfert des perturbations sur l’erreur d’observation.

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