Abstract
This paper investigates the problem of constructing an observer that asymptotically estimates a linear function of the state of a linear plant with state jumps in the presence of unknown inputs. Suitable geometric notions are introduced and discussed in order to deal with this problem. A complete characterization of its solvability, together with a procedure for constructing the observer, is given in geometric terms. A sufficient solvability condition that can be practically checked by a simple procedure is also illustrated. Under mildly restrictive hypothesis, the necessary and sufficient solvability conditions can be practically checked and the observer can be practically constructed.
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