Geometric algorithms for zero cancellation with application to unknown-state, unknown-input reconstruction

This work deals with zero cancellation in discrete-time linear multivariable systems and its application to unknown-state unknown-input reconstruction. The problem is first tackled by considering a scheme based on the use of a feedforward compensator, then an equivalent cascade filter is obtained by means of duality arguments. The precompensator devised preserves crucial properties of the original system like reachability and right-invertibility, while the cascade filter maintains observability and left-invertibility and, therefore, is the appropriate solution to be exploited in connection with state and input reconstructors. The design method relies on the geometric approach. Two solutions, ensuing from different choices of the resolving subspace, are examined for the feedforward compensator and, consequently, its dual counterpart: the most convenient for its impact on reconstruction is then pursued.