Strong detectability and observers for linear time-varying systems (Q2107636)

In this present work the authors have introduced the notion of uniform strong\(^*\) detectability and an unknown input observer design procedure for linear time-varying systems. The proposed observer design allows to asymptotically reconstruct the system states in the presence of arbitrary unknown inputs. It can be seen as a generalization of the ideas for a linear time-invariant observer design presented in [\textit{M. E. Valcher}, IEEE Trans. Autom. Control 44, No. 2, 397--401 (1999; Zbl 0958.93018); \textit{M. Hou} and \textit{P. C. Müller}, IEEE Trans. Autom. Control 37, No. 6, 871--875 (1992; Zbl 0775.93021)]. Strong\(^*\) detectability is defined via the existence of an observer with a uniformly exponentially stable estimation error dynamics. It is shown that other strong\(^*\) detectability concepts, which are equivalent in a time-invariant setting, are not equivalent for time-varying systems. Examples of rigid body dynamics and Lorenz'96 model are provided to illustrate the results.