A unified algorithmic setting for signal-decoupling compensators and unknown-input observers

A standard geometric-type environment, where only the very basic tools of the geometric approach are used (those supported by well-settled and well-tested computational aids) enables the development of algorithms for numerous control and estimation problems in the discrete-time case. These are: measurable or previewed signal localization problems, perfect or almost perfect tracking (right inversion), and, by duality, perfect or almost perfect unknown input estimation with possible post-knowledge and input reconstruction (left inversion). It is also shown that the devices obtained (compensator and observer), that may be noncausal when specific stability requirements are not met, can be implemented as dynamical systems including finite-horizon convolutors or finite impulse response systems