Synthesis of Functional Unknown Input Observers for LTV and MIMO LTI Systems with Arbitrary Relative Degree

This article focuses on the development of functional unknown input observers for systems with arbitrary relative degree. Two distinct approaches are presented to address this challenge. The first approach is tailored to a class of time-varying systems expressed in a canonical controllable form. This method leverages the Generalized Parameter Estimation-Based Observer framework. The article derives the conditions for applicability of this solution and outlines the limitations on the number of estimable state variables. The second approach targets multi-input multi-output systems. In contrast to existing methods, the proposed solution is applicable to systems with arbitrary relative degree, significantly broadening its scope of application. The theoretical results are validated through simulation studies, which demonstrate the effectiveness of the proposed observers.