Strong Detectability and Observers for Linear Time Varying Systems

TL;DR

This paper introduces a new concept of strong detectability for linear time-varying systems with unknown inputs, enabling a straightforward observer design using Kalman filter techniques.

Contribution

It establishes the equivalence of strong detectability to auxiliary system detectability, simplifying observer design for systems with unknown inputs.

Findings

Observer design reduces to solving a differential Riccati equation.

The proposed method effectively estimates states in the presence of unknown inputs.

Numerical example demonstrates the approach's practical efficacy.

Abstract

This work presents a notion of strong detectability for linear time varying systems affected by unknown inputs. It is shown that this notion is equivalent to detectability of an auxiliary system without unknown inputs. This allows a straightforward observer design for dependable state estimation in the presence of unknown inputs. The design reduces to a deterministic Kalman filter design problem, where the observer gains can be obtained from the solution of a differential Riccati equation. The efficacy of the proposed approach is demonstrated by means of a numerical example.