CNRS Laboratory of Signals & Systems

GIF SUR YVETTE, France

CNRS Laboratory of Signals & Systems

GIF SUR YVETTE, France
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Carron R.,Aix - Marseille University | Carron R.,French Institute of Health and Medical Research | Chaillet A.,CNRS Laboratory of Signals & Systems | Chaillet A.,University Paris - Sud | And 6 more authors.
Frontiers in Systems Neuroscience | Year: 2013

High-frequency deep brain stimulation is used to treat a wide range of brain disorders, like Parkinson's disease. The stimulated networks usually share common electrophysiological signatures, including hyperactivity and/or dysrhythmia. From a clinical perspective, HFS is expected to alleviate clinical signs without generating adverse effects. Here, we consider whether the classical open-loop HFS fulfills these criteria and outline current experimental or theoretical research on the different types of closed-loop DBS that could provide better clinical outcomes. In the first part of the review, the two routes followed by HFS-evoked axonal spikes are explored. In one direction, orthodromic spikes functionally de-afferent the stimulated nucleus from its downstream target networks. In the opposite direction, antidromic spikes prevent this nucleus from being influenced by its afferent networks. As a result, the pathological synchronized activity no longer propagates from the cortical networks to the stimulated nucleus. The overall result can be described as a reversible functional de-afferentation of the stimulated nucleus from its upstream and downstream nuclei. In the second part of the review, the latest advances in closed-loop DBS are considered. Some of the proposed approaches are based on mathematical models, which emphasize different aspects of the parkinsonian basal ganglia: excessive synchronization, abnormal firing-rate rhythms, and a deficient thalamo-cortical relay. The stimulation strategies are classified depending on the control-theory techniques on which they are based: adaptive and on-demand stimulation schemes, delayed and multi-site approaches, stimulations based on proportional and/or derivative control actions, optimal control strategies. Some of these strategies have been validated experimentally, but there is still a large reservoir of theoretical work that may point to ways of improving practical treatment. © 2013 Carron, Chaillet, Filipchuk, Pasillas-Lépine and Hammond.


Monaco S.,University of Rome La Sapienza | Normand-Cyrot D.,CNRS Laboratory of Signals & Systems | Mattioni M.,University of Rome La Sapienza
IEEE Transactions on Automatic Control | Year: 2017

In this technical note, we show that Immersion and Invariance is a natural framework for the design of sampled-data stabilizing controllers for input-delayed systems. Assuming the existence of a continuous-time feedback in the delay free case, Immersion and Invariance stabilizability of the equivalent sampled-data dynamics is proven. The proof is constructive for the stabilizing controller. Two simulated examples illustrate the performances. © 1963-2012 IEEE.


Mazenc F.,French Institute for Research in Computer Science and Automation | Niculescu S.-I.,EPI DISCO | Bekaik M.,CNRS Laboratory of Signals & Systems
IEEE Transactions on Automatic Control | Year: 2013

We address the problem of stabilizing systems belonging to a family of time-varying nonlinear systems with distributed input delay through state feedbacks without retarded term. The approach we adopt is based on a new technique that is inspired by the reduction model technique. The control laws we obtain are nonlinear and time-varying. They globally uniformly exponentially stabilize the origin of the considered system. We illustrate the construction with a networked control system. © 2012 IEEE.


Mazenc F.,Supelec | Normand-Cyrot D.,CNRS Laboratory of Signals & Systems
IEEE Transactions on Automatic Control | Year: 2013

We propose a new construction of exponentially stabilizing sampled feedbacks for continuous-time linear time-invariant systems with an arbitrarily large constant pointwise delay in the inputs. Stability is guaranteed under an assumption on the size of the largest sampling interval. The proposed design is based on an adaptation of the reduction model approach. The stability of the closed loop systems is proved through a Lyapunov functional of a new type, from which is derived a robustness result. © 1963-2012 IEEE.


Mazenc F.,Supelec | Niculescu S.-I.,CNRS Laboratory of Signals & Systems | Bekaik M.,Supelec
Proceedings of the IEEE Conference on Decision and Control | Year: 2011

We propose a new solution to the problem of globally asymptotically stabilizing a nonlinear system in feedback form with a known pointwise delay in the input. The result covers a family of systems wider than those studied in the literature and endows with control laws with a single delay, in contrast to the existing one, which include two distinct pointwise delays or distributed delays. The design strategy is based on the construction of an appropriate Lyapunov-Krasovskii functional. © 2011 IEEE.


Renzo M.D.,CNRS Laboratory of Signals & Systems | Haas H.,University of Edinburgh
IEEE Transactions on Communications | Year: 2011

In this paper, we study the performance of Space Shift Keying (SSK) modulation for a generic MultipleInputMultipleOutput (MIMO) wireless system over correlated Rician fading channels. In particular, our contribution is twofold. i) First, we propose a very general framework for computing the Average Bit Error Probability (ABEP) of SSKMIMO systems over a generic Rician fading channel with arbitrary correlation and channel parameters. The framework relies upon the Moschopoulos method. We show that it is exact for MIMO systems with two transmitantenna and arbitrary receiveantenna, while an asymptoticallytight upperbound is proposed to handle the system setup with an arbitrary number of transmitantenna. ii) Second, moving from the consideration that conventional SSKMIMO schemes can offer only receivediversity gains, we propose a novel SSKMIMO scheme that can exploit the transmitantenna to increase the diversity order. The new method has its basic foundation on the transmission of signals with good timecorrelation properties, and is called TimeOrthogonalSignalDesign (TOSD) assisted SSK modulation (TOSDSSK). It is shown that the proposed method can increase twofold the diversity order for arbitrary transmit and receiveantenna. In particular, for MIMO systems with two transmitantenna and Nr receiveantenna fulldiversity equal to 2N-r can be achieved. Analytical frameworks and theoretical findings are substantiated via Monte Carlo simulations for various system setups. © 2011 IEEE.


Mazenc F.,CNRS Laboratory of Signals & Systems | Bernard O.,French Institute for Research in Computer Science and Automation
International Journal of Robust and Nonlinear Control | Year: 2014

Designing an interval observer with stability properties for nonlinear systems, which are not cooperative and not globally Lipschitz, is an open problem. This paper studies a general canonical structure for which interval observers with input to state stability (ISS) properties can be derived. This canonical block triangular nonlinear structure is rather general and may result from a change of coordinates or an output injection. We provide a general method for explicitly constructing framers for systems for which can be given such a structure. We also construct ISS interval observers when additional properties are satisfied. The systems we consider are in general not cooperative and not globally Lipschitz. We illustrate the constructions by designing a framer and an ISS interval observer for two models of bioreactors. © 2012 John Wiley & Sons, Ltd.


Bondon P.,CNRS Laboratory of Signals & Systems
Conference Record - Asilomar Conference on Signals, Systems and Computers | Year: 2013

The problem of estimating an autoregressive conditionally heteroscedastic (ARCH) model in the presence of missing data is investigated. A two-stage least squares estimator which is easy to calculate is proposed and its strong consistency and asymptotic normality are established. The behaviour of the estimator for finite samples is analyzed via Monte Carlo simulations, and is compared to a Yule-Walker estimator and to some estimators based on a complete data set obtained after filling the missing observations by imputation procedures. An application to real data is also reported. © 2013 IEEE.


Mazenc F.,French Institute for Research in Computer Science and Automation | Dinh T.N.,French Institute for Research in Computer Science and Automation | Niculescu S.I.,CNRS Laboratory of Signals & Systems
Proceedings of the IEEE Conference on Decision and Control | Year: 2012

First, time-invariant interval observers are proposed for a family of nonlinear systems. Second, it is shown that, for any time-invariant exponentially stable discrete-time linear system with additive disturbances, time-varying exponentially stable discrete-time interval observers can be constructed. The result relies on the design of time-varying changes of coordinates which transform a linear system into a nonnegative linear system. © 2012 IEEE.


Li X.-G.,Northeastern University China | Niculescu S.-I.,CNRS Laboratory of Signals & Systems | Cela A.,School of Engineering in Information and Communication Science and Technology | Wang H.-H.,Northeastern University China | Cai T.-Y.,Northeastern University China
IEEE Transactions on Automatic Control | Year: 2013

Obtaining the Puiseux series of multiple imaginary (characteristic) roots (MIRs) is a fundamental issue in the stability analysis of timedelay systems. However, to the best of the authors' knowledge, this issue has not been fully investigated up to date. This note focuses on the Puiseux series expansion of MIRs of linear time-invariant systems including commensurate delays. For anMIR of anymultiplicity, we propose an algorithm for defining the structure of the Puiseux series, as well as the explicit computation of the corresponding coefficients. By using the proposed method, we can find all the Puiseux series corresponding to all the root loci. © 2012 IEEE.

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