L2-stability criterion for systems with decentralized asynchronous controllers

International audienceThis paper deals with the stability analysis of decentralized sampled-data Linear Time Invariant (LTI) control systems with asynchronous sensors and actuators. We consider the case where each controller in the decentralized setting has its own sampling and actuation frequency which translates to asynchrony between sensors and actuators. The errors induced due to sampling and asynchronicity are modelled using two different operator approaches, leading to simple L2-stability criteria for the overall decentralized control system. The simplicity of the obtained criteria is illustrated by an example and simulation results exhibit the effectiveness of the approach

Exponential Synchronization of Nonlinear Oscillators Under Sampled-Data Coupling

This paper presents a novel approach towards synchronization analysis of nonlinear oscillatory systems, bidi-rectionally coupled via a networked communication channel. The system under consideration is a two-agent nonlinear system, under the constraint that information is transmitted between the two systems using a sampled-data communication strategy that could be periodic or aperiodic. The networked system dynamics is remodelled as a feedback-interconnection of a continuous-time system, and an operator that accounts for the communication constraints. By studying the properties of this feedback-interconnection in the framework of dissipativity theory, we provide a novel criterion that guarantees exponential synchronization. The provided criterion also aids in deciding the trade-off between a bound on the sampling intervals, the coupling gain, and the desired transient rate of synchronization. Finally, the theoretical results are illustrated using a two-agent Fitzhugh-Nagumo system

Dissipativity based stability criterion for aperiodic sampled-data systems subject to time-delay

International audienceThis extended abstract presents a dissipativity-based stability analysis of Linear Time Invariant (LTI) systems subjected to aperiodic sampling and time-varying delay. We provide a novel stability criterion which aids in making the trade-offs between maximum allowable sampling interval and delays while guaranteeing stability. Simulation results have been provided to demonstrate the effectiveness of the proposed criterion

Dissipativity-based Framework for Stability Analysis of Aperiodically Sampled Nonlinear Systems with Time-varying Delay

International audienceIn this paper, we provide novel conditions for stability analysis of aperiodically sampled nonlinear control systems subjected to time-varying delay. The proposed approach can also deal with cases in which delay is larger than the sampling interval. It is applicable to a general class of nonlinear systems and provides sufficient criteria for stability that aid in making trade-offs between control performance and the bounds on sampling interval and delay. As a stepping stone, a preliminary and generic result based on dissipativity, is introduced to analyse the exponential stability of a class of feedback-interconnected systems. The nonlinear sampled-data system is remodelled to consider the effects of sampling and delay in the dissipativity framework, as perturbations to the nominal closed-loop system. This leads to constructive stability conditions for a continuous time closed-loop system given by the feedback interconnection of the nominal closed-loop system and an operator(s) that captures the effects of sampling and delay. For Linear Time-Invariant (LTI) systems, we recover simple Linear Matrix Inequality (LMI) and frequency domain conditions previously proposed in the robust control framework

Exponential Synchronization of Nonlinear Oscillators Under Sampled-Data Coupling

International audienceThis paper presents a novel approach towards synchronization analysis of nonlinear oscillatory systems, bidi-rectionally coupled via a networked communication channel. The system under consideration is a two-agent nonlinear system, under the constraint that information is transmitted between the two systems using a sampled-data communication strategy that could be periodic or aperiodic. The networked system dynamics is remodelled as a feedback-interconnection of a continuous-time system, and an operator that accounts for the communication constraints. By studying the properties of this feedback-interconnection in the framework of dissipativity theory, we provide a novel criterion that guarantees exponential synchronization. The provided criterion also aids in deciding the trade-off between a bound on the sampling intervals, the coupling gain, and the desired transient rate of synchronization. Finally, the theoretical results are illustrated using a two-agent Fitzhugh-Nagumo system

Frequency-Domain Stability Conditions for Asynchronously Sampled Decentralized LTI Systems

International audienceThis paper deals with the exponential stability analysis of decentralized, sampled-data, Linear Time Invariant (LTI) control systems with asynchronous sensors and actuators. We consider the case where each controller in the decentralized setting has its own sampling and actuation frequency, which translates to asynchrony between sensors and actuators. Additionally, asynchrony may be induced by delays between the sampling instants and actuation update instants as relevant in a networked context. The decentralized, asynchronous LTI system is represented as the feedback interconnection of a continuous-time LTI system operator and an operator that captures the effects of asynchrony induced by sampling and delay. By characterizing the properties of the operators using small-gain type Integral Quadratic Constraints (IQC), we provide criteria for exponential stability of the asynchronous, decentralized LTI state-space models. The approach provided in this paper considers two scenarios, namely the 'large-delay' case and the 'small-delay' case where the delays are larger and smaller than the sampling interval, respectively. The effectiveness of the proposed results is corroborated by a numerical example

Networked Dynamical Systems : An Input-Output Approach Towards Stability and Synchronization Analysis

Recent advances in communication technology have given rise to a wide range of appli-cations for networked engineering systems such as, e.g., transportation systems, powergrids, cooperative robotics, etc., in which systems, sensors, actuators and controllersare linked over a (wireless) communication network. In such networked systems, in-formation transmission over the network is not continuous (sampling effect), delayedand often asynchronous. A well-known challenge in this context is that sampling anddelay effects induced by the communication network can render systems unstableand destroy synchronization properties in. The main contribution of this thesis is the development of novel modelling and analysis tools for stability and synchronizationanalysis in complex networked systems, while considering asynchronous, aperiodicsampling and delay effects. To that end, this thesis exploits the Input-Output ap-proach, which is well known to be appealing from an engineering perspective. Theproposed analysis tools aid in obtaining a trade-off between, on the one hand, system performance requirements (guaranteeing system stability and synchronizationproperties), and, on the other hand, communication network requirements (samplingperiod and delay bounds).La révolution des technologies de communication a généré de nombreuses opportunités applicatives mettant en œuvre une ing ́énierie de réseaux et systèmes: systèmes de transport, réseaux de distribution électrique, robotique coopérative, etc. Dans chacun de ces domaines, des processus, des capteurs, des actionneurs et des contrôleurs sont connectés à travers un réseau de communication. Dans ce contexte de multi-agents connectés, les effets d’ échantillonnage (digitalisation) et de retards (qualité de service du réseau) ont été clairement identifiés comme des dynamiques additionnelles sources d’instabilité ou de de synchronisation du réseau. La principale contribution de cette thèse est le d développement de nouveaux outils de modélisation et d’analyse permettant de garantir la stabilité ou la synchronisation de systèmes en réseau, tout en tenant compte des effets complexes d’asynchronisme des échantillonneurs (non périodiques) et de retard dans le réseau. Ainsi, en se plaçant dans un contexte entrée-sortie, nous proposons une nouvelle approche de modélisation et d’analyse de stabilité. Les outils ainsi définis permettent d’obtenir un compromis entre, d’une part,les performances requises pour la dynamique du système contrôle (stabilité, convergence exponentielle/rapidité, synchronisation) et, d’autre part, des caractéristiques temporelles du réseau (bornes des intervalles de variation des échantillonnages et des retards) liées à sa qualité de service

Exponential Synchronization of Nonlinear Oscillators under Sampled-Data Coupling

This paper presents a novel approach towards synchronization analysis of nonlinear oscillatory systems, bidirectionally coupled via a networked communication channel. The system under consideration is a two-agent nonlinear system, under the constraint that information is transmitted between the two systems using a sampled-data communication strategy that could be periodic or aperiodic. The networked system dynamics is remodelled as a feedback-interconnection of a continuous-time system, and an operator that accounts for the communication constraints. By studying the properties of this feedback-interconnection in the framework of dissipativity theory, we provide a novel criterion that guarantees exponential synchronization. The provided criterion also aids in deciding the trade-off between a bound on the sampling intervals, the coupling gain, and the desired transient rate of synchronization. Finally, the theoretical results are illustrated using a two-agent Fitzhugh-Nagumo system

L2-stability criterion for systems with decentralized asynchronous controllers

International audienceThis paper deals with the stability analysis of decentralized sampled-data Linear Time Invariant (LTI) control systems with asynchronous sensors and actuators. We consider the case where each controller in the decentralized setting has its own sampling and actuation frequency which translates to asynchrony between sensors and actuators. The errors induced due to sampling and asynchronicity are modelled using two different operator approaches, leading to simple L2-stability criteria for the overall decentralized control system. The simplicity of the obtained criteria is illustrated by an example and simulation results exhibit the effectiveness of the approach

{L}-{2}-stability criterion for systems with decentralized asynchronous controllers

This paper deals with the stability analysis of decentralized sampled-data Linear Time Invariant (LTI) control systems with asynchronous sensors and actuators. We consider the case where each controller in the decentralized setting has its own sampling and actuation frequency which translates to asynchrony between sensors and actuators. The errors induced due to sampling and asynchronicity are modelled using two different operator approaches, leading to simple \mathcal{L}-{2}-stability criteria for the overall decentralized control system. The simplicity of the obtained criteria is illustrated by an example and simulation results exhibit the effectiveness of the approach