High-gain observer design for multi-output systems: Transformation to a canonical form by dynamic output shaping

In this paper we consider the observer design problem for a class of observable linear systems perturbed by nonlinear, time-varying terms. Our design methodology is based on a canonical form, similar to canonical forms used elsewhere in the literature, that allows the nonlinearities to be dominated using high gain. We show that linear state and output transformations to this canonical form exist if, and only if, the data of the system satisfies a certain admissibility property. Moreover, the appropriate transformations can easily be constructed using available tools. We furthermore show that, if a system does not satisfy the admissibility property, it may be possible to extend it with an invertible output filter that makes the data of the extended system admissible. We refer to the problem of constructing such a filter as the output shaping problem and introduce an algorithm that solves the problem whenever it is solvable. Copyright c 0000 John Wiley & Sons, Ltd.