Asymptotic observers for weighted evolution equations in banach spaces — A nonlinear approach

We consider in an arbitrary reflexive Banach space X. the nonlinear system (1) where the control u ϵ L^∞ ([0. +∞[, R⁺) multiplies a m-dissipative linear operator A. The operator B is nonlinear dissipative. and y stands for the output of the system. We prove in our framework, the existence of a general suitable nonlinear asymptotic time dependent observer, including the classical Luenberger observer. For this purpose, we show that the usual notions of regularly persistent inputs proposed in [9] or [3] are the appropriate concepts that allow to generalize the main results of [11], [12] or [9] for bilinear systems to our general nonlinear ones.