Partial State and InputObservers for Linear Systemswith Unknown Inputs!

In this paper, we consider the problem of constructing partial state and input observers for linear systems with unknown inputs. Specifically, we develop a design procedure that characterizes the set of all linear functions of the states and inputs that can be reconstructed through a linear observer. Our design procedure directly produces the corresponding observer parameters, and also encompasses delayed observers, which increases the number of linear functionals that can be reproduced. In comparison to previous work on partial state and input observers, the main contributions of our work are (i) an algebraic procedure to design delayed linear observers with dimension no greater than that of the system, and (ii) a unified treatment of both state and input observers, along with a characterization of the stability of these observers. The observers obtained using our procedure can be used in applications such as fault diagnosis and control system design for uncertain systems