Système invariant

Résumé

Un processus transformant un signal d’entrée en un signal de sortie (signaux électriques par exemple) est appelé système invariant (ou stationnaire) lorsqu’une translation du temps appliquée à l’entrée se retrouve à la sortie. Dans ce sens, la sortie ne dépend pas explicitement du temps. Définition Si au signal d'entrée \displaystyle x(t), un système invariant associe une sortie \displaystyle y(t), alors quel que soit le décalage temporel \displaystyle \delta appliqué à l'entrée, le système associe au signal \tilde x(t) = x(t + \delta) la sortie décalée \tilde y(t) = y(t + \delta). Définition équivalente : Un système est invariant s’il y a commutativité entre le bloc du système et un bloc délai arbitraire. Cette propriété peut être satisfaite (mais pas nécessairement) si la fonction de transfert du système n'est pas une fonction du temps (hormis dans les expressions de l'entrée et de la sortie).

Source officielle

https://fr.wikipedia.org/wiki/Syst%C3%A8me_invariant

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Victor Constantin, Pascal Fua, Sina Honari, Helge Jochen Rhodin, Mathieu Salzmann

In this paper we propose an unsupervised feature extraction method to capture temporal information on monocular videos, where we detect and encode subject of interest in each frame and leverage contrastive self-supervised (CSS) learning to extract rich latent vectors. Instead of simply treating the latent features of nearby frames as positive pairs and those of temporally-distant ones as negative pairs as in other CSS approaches, we explicitly disentangle each latent vector into a time-variant component and a time-invariant one. We then show that applying contrastive loss only to the time-variant features and encouraging a gradual transition on them between nearby and away frames while also reconstructing the input, extract rich temporal features, well-suited for human pose estimation. Our approach reduces error by about 50% compared to the standard CSS strategies, outperforms other unsupervised single-view methods and matches the performance of multi-view techniques. When 2D pose is available, our approach can extract even richer latent features and improve the 3D pose estimation accuracy, outperforming other state-of-the-art weakly supervised methods.

2022

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Fixed-structure H-2 controller design for polytopic systems via LMIs

Alireza Karimi, Arash Sadeghzadeh

In this paper a new approach for fixed-structure H2 controller design in terms of solutions to a set of linear matrix inequalities are given. Both discrete- and continuous-time single-input single-output (SISO) time- invariant systems are considered. Then the results are extended to systems with polytopic uncertainty. The presented methods are based on an inner convex approximation of the non-convex set of fixed-structure H2 controllers. The designed procedures initialized either with a stable polynomial or with a stabilizing controller. An iterative procedure for robust controller design is given that converges to a suboptimal solution. The monotonic decreasing of the upper bound on the H2 norm is established theoretically for both nominal and robust controller design.

Wiley-Blackwell2015

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Generalized sampling consists in the recovery of a function f, from the samples of the responses of a collection of linear shift-invariant systems to the input f . The reconstructed function is typically a member of a finitely generated integer-shift invariant space that can reproduce polynomials up to a given degree M. While this property allows for an approximation power of order (M + 1), it comes with a tradeoff on the length of the support of the basis functions. Specifically, we prove that the sum of the length of the support of the generators is at least (M+1). Following this result, we introduce the notion of shortest basis of degree M, which is motivated by our desire to minimize computational costs. We then demonstrate that any basis of shortest support generates a Riesz basis. Finally, we introduce a recursive algorithm to construct the shortest-support basis for any multi-spline space. It provides a generalization of both polynomial and Hermite B-splines. This framework paves the way for novel applications such as fast derivative sampling with arbitrarily high approximation power. (C) 2021 Elsevier B.V. All rights reserved.

2021

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