Strong Observability of LTV Systems With Feedthrough and On-Orbit Reconnaissance and Evasion Applications

Abstract

This letter considers linear time-varying control systems with feedthrough. A necessary and sufficient condition for strong observability (also known as observability with unknown inputs) is stated in terms of the observability matrix and newly redefined invertibility matrix. This is followed by an observer for pointwise reconstruction of the state from the output and its time derivatives. A variable-time weakly unobservable subspace is then introduced such that the rank test can be recast in terms of this subspace and the kernel of a certain matrix. The subspace characterization leads to results on the existence and construction of unobservable state and control functions. The theoretical results are illustrated in an on-orbit reconnaissance application. Within the context of a time-varying relative orbital motion model, it is shown that strong observability is satisfiable with any constant or bounded feedthrough matrix. In the absence of strong observability, control functions to evade observation are constructed.