On the necessity of looped-functionals arising in the analysis of pseudo-periodic,sampled-data and hybrid systems

Looped-functionals have been shown to be relevant for the analysis of a wide variety of systems. However, the conditions obtained in previous papers on the analysis of sampled-data, impulsive and switched systems have only been shown to be sufficient for the characterisation of their associated discrete-time stability conditions. We prove here that these conditions are also necessary. This result is derived for a wider class of linear systems, referred to as impulsive pseudo-periodic systems, that encompass periodic, impulsive, sampled-data and switched systems as special cases.     

Wirtinger-based integral inequality: Application to time-delay systems

In the last decade, the Jensen inequality has been intensively used in the context of time-delay or sampled-data systems since it is an appropriate tool to derive tractable stability conditions expressed in terms of linear matrix inequalities (LMIs). However, it is also well-known that this inequality introduces an undesirable conservatism in the stability conditions and looking at the literature, reducing this gap is a relevant issue and always an open problem. In this paper, we propose an alternative inequality based on the Fourier Theory, more precisely on the Wirtinger inequalities. It is shown that this resulting inequality encompasses the Jensen one and also leads to tractable LMI conditions. In order to illustrate the potential gain of employing this new inequality with respect to the Jensen one, two applications on time-delay and sampled-data stability analysis are provided.     

Textural Changes of Natural Cheddar Cheese During the Maturation Process

ABSTRACT: Texture parameters of commercial natural cheddar cheese were tracked over the maturation period (11-mo) but not to evaluate optimal or desirable characteristics. Large strain analysis was performed using the TA-XT2 Texture Analyzer. Monitoring of chemical composition and degree of proteolysis and the solid proportions of milk fat were undertaken with differential scanning calorimeter. Fracture properties, force, and degree of compression confirmed a reduction in cheese firmness and an increase in cheese crumbliness during maturation. Increases in the concentration of small peptides, indicating enhanced proteolytic activity, and an increase in the proportion of solid fat at 21 °C late in maturation were considered primarily responsible for the changes recorded in cheese texture.     

Real-time control systems: feedback,scheduling and robustness

The efficient control of real-time distributed systems, where continuous components are governed through digital devices and communication networks, needs a careful examination of the constraints arising from the different involved domains inside co-design approaches. Thanks to the robustness of feedback control, both new control methodologies and slackened real-time scheduling schemes are proposed beyond the frontiers between these traditionally separated fields. A methodology to design robust aperiodic controllers is provided, where the sampling interval is considered as a control variable of the system. Promising experimental results are provided to show the feasibility and robustness of the approach.     

Stability analysis of time‐delay systems via Bessel inequality: A quadratic separation approach

In this paper, new sufficient stability conditions for the asymptotic stability of time‐delay systems are presented using the quadratic separation approach. The time‐delay system is modeled as an interconnected closed‐loop system involving a linear transformation and delay‐dependent functions, representing the uncertainties brought by the delay. Those complex‐valued functions are then embedded into adequate norm‐bounded uncertainties, which lead to several stability results. The novelty of this approach relies on the introduction of new dedicated functions that are built in accordance to the Bessel inequality. They allow us to model the system as an uncertain feedback system and to control the accuracy of the inequality. Then, a sequence of linear matrix inequality conditions is proposed, which tends to the analytical bounds for both delay‐dependent stability and delay range stability, at least on examples.     

A novel stability analysis of linear systems under asynchronous samplings

This article proposes a novel approach to assess the stability of continuous linear systems with sampled-data inputs. The method, which is based on the discrete-time Lyapunov theorem, provides easy tractable stability conditions for the continuous-time model. Sufficient conditions for asymptotic and exponential stability are provided dealing with synchronous and asynchronous samplings and uncertain systems. An additional stability analysis is provided for the cases of multiple sampling periods and packet losses. Several examples show the efficiency of the method.     

A periodic approach for input‐delay problems: Application to network controlled systems affected by polytopic uncertainties

This paper deals with robust stability and stabilization of linear discrete‐time systems subject to uncertainties and network constraints. In network control systems, the control loop is closed over a network, which induces additional dynamics to the original control loop such as delays, sampling, and quantization among many others. This paper focuses on networked induced delays due to unreliable network for which packet losses may occur. An equivalent periodic‐like representation of the resulting system is proposed. This allows first to revisit existing results in this framework and second to take model uncertainties into account by analyzing the closed‐loop model by means of a recent method based on robust control for discrete‐time time‐varying systems. Stability analysis and dynamic state‐feedback stabilization are characterized via new conditions, whose conservatism is extensively discussed. Effectiveness of the proposed methodology is illustrated by numerical examples. Copyright © 2015 John Wiley & Sons, Ltd.     

Improved stability conditions for discrete‐time systems under dynamic network protocols

This paper deals with the stability of discrete‐time networked systems with multiple sensor nodes under dynamic scheduling protocols. Access to the communication medium is orchestrated by a weighted try‐once‐discard or by an independent and identically‐distributed stochastic protocol that determines which sensor node can access the network at each sampling instant and transmit its corresponding data. Through a time‐delay approach, a unified discrete‐time hybrid system with time‐varying delays in the dynamics and in the reset conditions is formulated under both scheduling protocols. Then, a new stability criterion for discrete‐time systems with time‐varying delays is proposed by the discrete counterpart of the second‐order Bessel‐Legendre integral inequality. The developed approach is applied to guarantee the stability of the resulting discrete‐time hybrid system model with respect to the full state under try‐once‐discard or independent and identically‐distributed scheduling protocol. The communication delays can be larger than the sampling intervals. Finally, the efficiency of the presented approach is illustrated by a cart‐pendulum system.     

Classification of incunable glyphs and out-of-distribution detection with joint energy-based models

Optical character recognition (OCR) has proved a powerful tool for the digital analysis of printed historical documents. However, its ability to localize and identify individual glyphs is challenged by the tremendous variety in historical type design, the physicality of the printing process, and the state of conservation. We propose to mitigate these problems by a downstream fine-tuning step that corrects for pathological and undesirable extraction results. We implement this idea by using a joint energy-based model which classifies individual glyphs and simultaneously prunes potential out-of-distribution (OOD) samples like rubrications, initials, or ligatures. During model training, we introduce specific margins in the energy spectrum that aid this separation and explore the glyph distribution’s typical set to stabilize the optimization procedure. We observe strong classification at 0.972 AUPRC across 42 lower- and uppercase glyph types on a challenging digital reproduction of Johannes Balbus’ Catholicon, matching the performance of purely discriminative methods. At the same time, we achieve OOD detection rates of 0.989 AUPRC and 0.946 AUPRC for OOD ‘clutter’ and ‘ligatures’ which substantially improves upon recently proposed OOD detection techniques. The proposed approach can be easily integrated into the postprocessing phase of current OCR to aid reproduction and shape analysis research.