Unknown Input Observer Design for Linear Time-Invariant Systems -- A Unifying Framework

TL;DR

This paper introduces a unifying framework for designing unknown input observers for linear time-invariant systems by transforming the system into a special coordinate basis, enabling flexible and property-dependent observer design.

Contribution

It proposes a novel transformation-based approach that unifies various observer design techniques for LTI systems with unknown inputs, considering system properties and convergence goals.

Findings

Provides a systematic design procedure for unknown input observers.

Reveals key system properties through the special coordinate basis.

Enables tailored observer design based on system observability and desired convergence.

Abstract

This paper presents a new observer design approach for linear time invariant multivariable systems subject to unknown inputs. The design is based on a transformation to the so-called special coordinate basis. This form reveals important system properties like invertability or the finite and infinite zero structure. Depending on the system's strong observability properties, the special coordinate basis allows for a straightforward unknown input observer design utilizing linear or nonlinear observers design techniques. The chosen observer design technique does not only depend on the system properties, but also on the desired convergence behavior of the observer. Hence, the proposed design procedure can be seen as a unifying framework for unknown input observer design.