Nonlinear unknown input observability and unknown input reconstruction: The general analytical solution

Nonlinear Unknown Input Observability: Analytical expression of the observable codistribution in the case of a single unknown input

Nonlinear Unknown Input Observability: Extension of the Observability Rank Condition and the Case of a Single Unknown Input

This paper investigates the unknown input observability problem in the nonlinear case under the assumption that the unknown inputs are differentiable functions of time (up to a given order). The goal is not to design new observers but to provide simple analytic conditions in order to check the weak local observability of the state. The analysis starts by extending the observability rank conditi...

Partial unknown input reconstruction for linear systems

The problem of partial unknown input (UI) reconstruction is addressed. It is considered that a linear functional of the UI vector has to be reconstructed using output information only. Necessary and sufficient conditions are given allowing for the reconstruction in finite time of the required UI’s; analogous conditions are obtained for the asymptotic reconstruction of the required UI’s. The sol...

Passivity and Unknown Input Observers for Nonlinear Systems

The main objective of this work is to study the relationship between passivity and existence of UIO in the nonlinear case. This work is motivated by two facts: On the one side by the well-known relationship between passivity and robustness in control theory. On the other side the equivalence previously found by one of the authors in the linear (square) case between three concepts: existence of ...

Geometric Insight and Structure Algorithms for Unknown-State, Unknown-Input Reconstruction in Linear Multivariable Systems

An algebraic approach to the synthesis of a dynamic system that reconstructs the generic inaccessible input of a discrete-time linear multivariable system with unknown initial state is discussed. The method devised exploits geometric properties of key subspaces for the original system and algebraic properties of the Moore-Penrose inverse of Toeplitz matrices related to the algorithms for comput...