Discrete-Time Normal Form for Left Invertibility Problem

This paper deals with the design of quadratic and higher order normal forms for the left invertibility problem. The linearly observable case and one-dimensional linearly unobservable case are investigated. The interest of such a study in the design of a delayed discrete-time observer is examined. The example of the Burgers map with unknown input is treated and a delayed discrete-time observer is designed. Finally, some simulated results are commented

Hypermetamorphosis in a leaf-miner allows insects to cope with a confined nutritional space

International audienceHypermetamorphosis has been described in several Lepidoptera leaf-miner species (mostly Gracillariidae, Epipyropidae, and Phyllocnistidae) and can be defined as a strong modification of the larval morphology associated with a switch in its feeding mode. Evolution of this larval feeding strategy presumably influences nutritional resources that can be exploited and has strong consequences for plant morphology. The following studyfocuses on Phyllonorycter blancardella (Lepidoptera: Gracillariidae), a leaf-miner developing on Malus domestica. We characterize the morphology of larval mouthparts and the resulting morphological impact on leaf tissues. Our results show that first instars do not strongly affect the leaf anatomy and leave most plant cells intact, while later instars significantly disrupt leaf tissues. Additionally, young larvae are ‘‘fluid-feeders’’ and feed on plant cell fluids resulting from the progression of the larvae through the lower layer of the leaf spongy parenchyma. They occupy a feeding niche clearly distinct from later instars that are ‘‘tissue-feeders’’. Hypermetamorphosis in P. blancardella most likely allows insects to cope with a confined nutritional space by partitioning the limited feeding resources, and may help leaf-miners to optimize their nutritio