On the Lyapunov Matrix of Linear Delay Difference Equations in Continuous Time

The fundamental matrix and the delay Lyapunov matrix of linear delay difference equations are introduced. Some properties of the Lyapunov matrix, and the jump discontinuities of its derivative are proven, leading to its construction in the case of single delay or commensurate delays. An approximation is proposed for the non-commensurate case

Necessary and sufficient stability conditions for integral delay systems

A Lyapunov-Krasovskii functional with prescribed derivative whose construction does not require the stability of the system is introduced. It leads to the presentation of stability/instability theorems. By evaluating the functional at initial conditions depending on the fundamental matrix we are able to present necessary and sufficient stability conditions expressed exclusively in terms of the delay Lyapunov matrix for integral delay systems. Some examples illustrate and validate the stability conditions.Comment: This paper has been submitted to International Journal of Robust and Nonlinear Contro

Stability analysis and estimate of the region of attraction of a human respiratory model

International audienceIn this paper, we complete the stability analysis of various human respiratory non-linear time delay models introduced in. More precisely, we present a detailed mathematical analysis of the stability of the nonlinear model trivial equilibrium , an estimate of its region of attraction and exponential estimates of the solutions starting in this region. The proposed approach is constructive and it is based on the use of Lyapunov-Krasovskii functionals of complete type for time-delay systems with a cross term in the time derivative

Assigning the Kronecker invariants of a matrix pencil by row or column completions

AbstractThe challenge consists in describing the relationships between the Kronecker invariants of a matrix pencil and one of its subpencils. For a given subpencil, an algorithm for constructing a matrix pencil with prescribed Kronecker invariants should also be proposed

Linear time-delay systems: the complete type functionals approach

[EN] Recent results on Lyapunov-Krasovskii functionals of complete type for linear time-delay systems are presented. The main concepts and results are introduced for the single delay system case, and necessary and sufficient stability conditions expressed in terms of the Lyapunov delay matrix are explained. The use of complete type functionals in analysis and controller design is discussed. The contribution focuses mainly at results of researchers in Mexico.[ES] Se introducen resultados recientes del enfoque de funcionales de Lyapunov-Krasovski de tipo completo para sistemas lineales con retardos. Se explican brevemente los principales conceptos y resultados para el caso de sistemas con un retardo así como las condiciones necesarias y suficientes de estabilidad expresadas en terminos del análogo de la matriz de Lyapunov. Las extensiones  de este tipo de condiciones de estabilidad a otras clases de sistemas con retardos son expuestas brevemente. Tambien se presentan aplicaciones existentes del efoque de funcionales de tipo completo a problemas de analisis y de diseño de controladores. El trabajo se enfoca a contribuciones de investigadores de Mexico a este tema de estudio.Este trabajo ha sido realizado parcialmente gracias al apoyo del Conacyt, México, Proyecto A1-S-24796.Mondié, S.; Gomez, M. (2022). Contribuciones al estudio de sistemas lineales con retardos: el enfoque de funcionales de tipo completo. Revista Iberoamericana de Automática e Informática industrial. 19(4):381-393. https://doi.org/10.4995/riai.2022.16828OJS38139319

Etiology, distribution, treatment modalities and complications of maxillofacial fractures

Purpose: This study evaluated the trends and factors associated with maxillofacial fractures treated from 1997 to 2007 in the Oral and Maxillofacial Surgery Department of the Clermont-Ferrand University Hospital. Material and Methods: This study included 364 patients of which 82% were men and 45%, 20-29-years old. The etio- logy, anatomical distribution, treatment modality and complications of maxillofacial fractures were examined. Results: Overall, interpersonal violence, traffic accidents and falls were the most common mechanisms of injury. There was a decreasing trend in traffic accidents and increasing one in falls as a cause of fracture over the 11-years period of this study. Young male patients were preferentially victim of interpersonal violence and traffic accidents, while middle-aged ones were of falls and work-related accidents. Middle-aged female patients were preferentially victim of traffic accidents and interpersonal violence, while older ones were of falls. And the number of fractures per patient varied according to the mechanism of injury: low after work-related accidents and high after traffic accidents. About two-third of fractures involved the mandible. Most of these mandibular fractures were treated by osteosynthesis with or without intermaxillary fixation, with the proportion of the latter increasing over time. There were very few postoperative infections and only in mandible. Conclusions: Maxillofacial fractures predominantly occur in young men, due to interpersonal violence. There is nevertheless an increasing trend in falls as a cause of fracture, especially in female patients, consistent with the increasing trend in presentation of older people. Most maxillofacial fractures involve the mandible and there is an increasing trend in treating these fractures by osteosynthesis without intermaxillary fixation. Antibiotic prophy - laxis associated with dental hygiene care can be indicated to prevent postoperative infections

Exponential Stabilization of a Class of Nonlinear Neutral Type Time-Delay Systems, an Oilwell Drilling Model Example

International audienceThis paper deals with exponential stabilization of the class of nonlinear neutral type time-delay systems that can be transformed into a multi-model system. The approach is based on Lyapunov-Krasovskii techniques and uses a descriptor representation. The exponential stability properties are proved using an appropriate change of variables associated with a polytopic representation. The results are given in terms of LMIs. As an application example, we determine an e ective stabilizing controller for an oilwell drilling system

Backstepping for Uncertain Nonlinear Systems with a Delay in the Control

International audienceThe recent new backstepping control design strategy based on the introduction of artificial delays and/or dynamic extensions is adapted to a family of systems. That way, globally asymptotically stabilizing control laws for fundamental systems which cannot be handled by other techniques are determined