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18362
01/01/2019

An overview of recent advances in stability of linear systems with time-varying delays

Q.L.HAN, X.M.ZHANG, A.SEURET, F.GOUAISBAUT, Y.HE

Swinburne, MAC

Revue Scientifique : IET Control Theory & Applications, Vol.13, N°1, 15p., Janvier 2019, doi 10.1049/iet-cta.2018.5188 , N° 18362

Lien : https://hal.laas.fr/hal-01920425

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Abstract

This paper provides an overview and in-depth analysis of rec ent advances in stability of linear systems with time-varyi ng delays. First, recent developments of a delay convex analys is approach, a reciprocally convex approach and the constru ction of Lyapunov-Krasovskii functionals are reviewed insightful ly. Second, in-depth analysis of the Bessel-Legendre inequ ality and some affine integral inequalities is made, and recent stability r esults are also summarized, including stability criteria f or three cases of a time-varying delay, where information on the bounds of the t ime-varying delay and its derivative is totally known, part ly known and completely unknown, respectively. Third, a number of stabi lity criteria are developed for the above three cases of the t ime-varying delay by employing canonical Bessel-Legendre inequalitie s, together with augmented Lyapunov-Krasovskii functiona ls. It is shown through numerical examples that these stability criteria o utperform some existing results. Finally, several challen ging issues are pointed out to direct the near future research.

145135
17044
01/01/2019

D-optimal design for multivariate polynomial regression via the Chrstoffel function and semidefinite relaxations

Y.DE CASTRO, F.GAMBOA, D.HENRION, R.HESS, J.B.LASSERRE

LM, Orsay, IMT, Toulouse, MAC

Revue Scientifique : Annals of Statistics, Vol.47, N°1, pp.127-155, Janvier 2019 , N° 17044

Lien : https://hal.laas.fr/hal-01483490

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We present a new approach to the design of D-optimal experiments with multivariate polynomial regressions on compact semi-algebraic design spaces. We apply the moment-sum-of-squares hierarchy of semidefinite programming problems to solve numerically and approximately the optimal design problem. The geometry of the design is recovered with semidefinite programming duality theory and the Christoffel polynomial.

145392
18428
21/12/2018

Error analysis of some operations involved in the Fast Fourier Transform

N.BRISEBARRE, M.M.JOLDES, J.M.MULLER, A.M.NANES, J.PICOT

LIP, Lyon, MAC, ENS Lyon, UTCLUJ

Rapport LAAS N°18428, Décembre 2018, 32p.

Lien : https://hal.archives-ouvertes.fr/hal-01949458

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We are interested in obtaining error bounds for the classical FFT algorithm in floating-point arithmetic, for the 2-norm as well as for the infinity norm. For that purpose we also give some results on the relative error of the complex multiplication by a root of unity, and on the largest value that can take the real or imaginary part of one term of the FFT of a vector x, assuming that all terms of x have real and imaginary parts less than some value b.

145731
18451
19/12/2018

Observability of Discrete-Time Linear Systems with Communication Protocols and Dropouts

A.TANWANI, R.JUNGERS, W.P.M.H.HEEMELS

MAC, UCL, Eindhoven

Manifestation avec acte : IEEE Conference on Decision and Control ( CDC ) 2018 du 17 décembre au 19 décembre 2018, Miami Beach (USA), Décembre 2018, 6p. , N° 18451

Lien : https://hal.laas.fr/hal-01951815

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We consider the problem of analyzing observability in discrete-time linear systems when the sensors, deployed in a distributed manner, may not communicate to an observer at once, and a protocol determines the communication pattern among different sensors. We use the formalism of automata to model the sequence of measurements determined by a protocol and show that the question of observability is decidable for the resulting system. We give upper bounds on the number of measurements required for deciding observability. In addition, we consider the effects of dropouts, which may occur in communicating the measurements across the channel. Again using the formalism of automatons to model certain classes of dropouts combined with the protocol, it is shown that observability is decidable in finite time for measurements sent across a communication channel using a protocol, and subject to dropouts.

145899
18580
19/12/2018

Unsafe Point Avoidance in Linear State Feedback

P.BRAUN, C.M.KELLETT, L.ZACCARIAN

Duisburg-Essen, EXT, MAC

Manifestation avec acte : IEEE Conference on Decision and Control ( CDC ) 2018 du 17 décembre au 19 décembre 2018, Miami (USA), Décembre 2018, pp.2372-2377 , N° 18580

Lien : https://hal.laas.fr/hal-01995607

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We propose a hybrid solution for the stabilization of the origin of a linear time-invariant stabilizable system with the property that a suitable neighborhood of a pre-defined unsafe point in the state space is avoided by the closed-loop solutions. Hybrid tools are motivated by the fact that the task at hand cannot be solved with continuous feedback, whereas the proposed hybrid solution induces nominal and robust asymptotic stability of the origin. More specifically, we formulate a semiglobal version of the problem at hand and describe a fully constructive approach under the assumption that the unsafe point to be avoided does not belong to the equilibrium subspace induced by the control input on the linear dynamics. The approach is illustrated on a numerical example

146743
18296
19/12/2018

Nonlinear control for an uncertain electromagnetic actuator

F.DESCHAUX, F.GOUAISBAUT, Y.ARIBA

MAC

Manifestation avec acte : IEEE Conference on Decision and Control ( CDC ) 2018 du 17 décembre au 19 décembre 2018, Miami (USA), Décembre 2018, 6p. , N° 18296

Lien : https://hal.laas.fr/hal-01868623

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This paper presents the design of a nonlinear control law for a typical electromagnetic actuator system. Electromagnetic actuators are widely implemented in industrial applications, and especially as linear positioning system. In this work, we aim at taking into account a magnetic phenomenon that is usually neglected: flux fringing. This issue is addressed with an uncertain modeling approach. The proposed control law consists of two steps, a backstepping control regulates the mechanical part and a sliding mode approach controls the coil current and the magnetic force implicitly. An illustrative example shows the effectiveness of the presented approach.

144677
18509
19/12/2018

Stability of distributed delay system with infinite support

Y.ARIBA, F.GOUAISBAUT, A.SEURET, K.LIU

MAC, CPPM

Manifestation avec acte : IEEE Conference on Decision and Control ( CDC ) 2018 du 17 décembre au 19 décembre 2018, Miami Beach (USA), Décembre 2018, 6p. , N° 18509

Lien : https://hal.laas.fr/hal-01962563

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This paper is devoted to the stability analysis of infinite distributed delay systems. The basic idea is to model the original time-delay system into an interconnected feedback system in order to use robust analysis and especially quadratic separation. This approach has been widely used to study classical pointwise time-delay system. The stability analysis is performed by introducing new quadratic inequalities based on Laguerre polynomials particularly well fitted to deal with infinite distributed delay. It allows to develop new stability results which accuracy depends on the chosen polynomial degree.

146153
18081
19/12/2018

Relaxed periodic switching controllers of high-frequency DC-DC converters using the δ-operator formulation

A.CUTILLAS, C.ALBEA SANCHEZ, A.SEURET, F.GORDILLO

Seville, MAC

Manifestation avec acte : IEEE Conference on Decision and Control ( CDC ) 2018 du 17 décembre au 19 décembre 2018, Miami Beach (USA), Décembre 2018, 6p. , N° 18081

Lien : https://hal.archives-ouvertes.fr/hal-01746435

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This paper deals with the design of new periodic switching control laws for high frequency DC-DC converters. The contributions are twofolds. On a first hand, the DC-DC converter model are rewritten as a periodic switched affine systems thanks to a δ-operator formulation, which represent an efficient framework for the numerical discretization at high frequencies. On a second hand, three different control laws are provided, the first one being the usual Lyapunov-based control law and the two others being relaxed versions of this first solution. The benefits of these two new control laws over the usual Lyapunov-based one are demonstrated on an simple example. More particularly, it is showed that the selection of sampling period and of the control law strongly influence the size of the region of attraction.

147718
18061
19/12/2018

Exponential Lyapunov Stability Analysis of a Drilling Mechanism

M.BARREAU, A.SEURET, F.GOUAISBAUT

MAC

Manifestation avec acte : IEEE Conference on Decision and Control ( CDC ) 2018 du 17 décembre au 19 décembre 2018, Miami Beach (USA), Décembre 2018, 6p. , N° 18061

Lien : https://hal.laas.fr/hal-01725416

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This article deals with the stability analysis of a drilling system which is modelled as a coupled ordinary differential equation / string equation. The string is damped at the two boundaries but leading to a stable open-loop system. The aim is to derive a linear matrix inequality ensuring the exponential stability with a guaranteed decay-rate of this interconnected system. A strictly proper dynamic controller based on boundary measurements is proposed to accelerate the system dynamics and its effects are investigated through the stability theorem and simulations. It results in an efficient finite dimension controller which subsequently improves the system performances.

144227
18454
19/12/2018

Max-Min Lyapunov Functions for Switching Differential Inclusions

M.DELLA ROSSA, A.TANWANI, L.ZACCARIAN

MAC

Manifestation avec acte : IEEE Conference on Decision and Control ( CDC ) 2018 du 17 décembre au 19 décembre 2018, Miami Beach (USA), Décembre 2018 , N° 18454

Lien : https://hal.archives-ouvertes.fr/hal-01951377

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We use a class of locally Lipschitz continuous Lyapunov functions to establish stability for a class of differential inclusions where the set-valued map on the right-hand-side comprises the convex hull of a finite number of vector fields. Starting with a finite family of continuously differentiable positive definite functions, we study conditions under which a function obtained by max-min combinations over this family of functions is a Lyapunov function for the system under consideration. For the case of linear systems, using the S-Procedure, our conditions result in bilinear matrix inequalities. The proposed construction also provides nonconvex Lyapunov functions, which are shown to be useful for systems with state-dependent switching that do not admit a convex Lyapunov function.

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