Unknown-input state observers for switching linear structured systems

This work deals with the problem of designing state observers in the presence of unknown inputs for switching linear structured systems – i.e., dynamical systems which consist of a finite indexed family of linear structured systems and a switching signal indicating the active system at each time instant. Switching linear structured systems lend themselves to be described both by families of parametric state space models and by families of directed graphs, in addition to the signal ruling the switching from one mode to another. Hence, the approach adopted herein is blended. It leverages on structural notions stemmed from the geometric approach and it exploits interpretations grounded on the graph theory. The notions of switching conditioned invariant subset and switching essential output injection play a key role in the derivation of the main result, a constructive necessary and sufficient condition for solvability of the unknown-input state observation problem. The methodological discussion is illustrated by two examples.