Integrability for Nonlinear Time-Delay Systems

In this note, the notion of integrability is defined for 1-forms defined in the time-delay context. While in the delay-free case, a set of 1-forms defines a vector space, it is shown that 1-forms computed for time-delay systems have to be viewed as elements of a module over a certain non-commutative polynomial ring. Two notions of integrability are defined, strong and weak integrability, which coincide in the delay-free case. Necessary and sufficient conditions are given to check if a set of 1-forms is strongly or weakly integrable. To show the importance of the topic, integrability of 1-forms is used to characterize the accessibility property for nonlinear time-delay systems. The possibility of transforming a system into a certain normal form is also considered

Effect of Biological Additives in Red Clover – Timothy Conservation

Red clover at early flower bud formation is difficult to ensile. For efficient improvement of the quality of leguminous silages, chemical additives are used. The present research focuses on the effectiveness of biological additives with different composition on the fermentation and quality of clover silage

Disturbance decoupling of time delay systems

International audienceA necessary and sufficient condition is derived for the solvability of the disturbance decoupling problem by pure shift dynamic compensator. It corrects previously obtained results for multi-input multi-output (MIMO) systems.Also, necessary and sufficient conditions are given for the solvability of the problem by dynamic compensator for SISO systems

Towards integrability for nonlinear time-delay systems

International audienceIn this paper the integrability of differential one-forms is studied in case of timedelays are present. Two notions, weak and strong integrability, are defined and the difference with delay-free case is explained. After giving the algorithms to check if some one-forms are strongly or weakly integrable, based on examples, the differences of the two notions of integrability are being studied. Finally, the role of integrability is explained when looking for a change of coordinates

Towards integrability for nonlinear time-delay systems

In this paper the integrability of differential one-forms is studied in case time-delays are present. Two notions, weak and strong integrability, are defined and the difference with delay-free case is explained. After giving the algorithms to check if some one-forms are strongly or weakly integrable, based on examples, the differences of the two notions of integrability are studied. Finally, the role of integrability is explained when looking for a change of coordinates together with an application to accessibility property