Mathematics

Given a nonlinear system, we have already studied (previous lecture) the observable cases where the state->output map is regular (they are of two types, according to the fact that the number of observations is larger or smaller than the number of controls). Now, we study the case where this state->output map is degenerate. As in the theory of differentiable functions, it looks that the right notion of a degenerate mapping is related to the notion of a "finite mapping". In all situations (the degenerate and the non degenerate one), we can construct nonlinear asymptotic observers, with prescribed arbitrary exponential convergence, and we can use them to stabilise asymptotically the system via dynamic output feedback.