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We study controlled systems which are uniformly observable and differentiallyobservable with an order larger than the system state dimension. We establishthat they may be transformed into a (partial) triangular canonical form butwith possibly non locally Lipschitz functions. We characterize the points wherethis Lipschitzness may be lost and investigate the link with uniforminfinitesimal observability.

On the triangular canonical form for uniformly observable controlled systems