Observation Problem for MIMO-Systems with Unknown Input under Degenerate Relative Degree

Abstract

We consider the problem of constructing a bounded error observer for a multivariate system with an unknown input. The input is assumed to be bounded uniformly in time by a known constant. We study the case in which the relative degree for the system is not defined. A generalization of this concept—a degenerate relative degree—is used to solve the problem. Based on this concept, we indicate a method for reducing system to a generalized form with distinguished zero dynamics (an analog of the normal form). Further, we construct an observer for a system in this form using a hierarchical high-gain feedback.