Non-recursive sequential input deconvolution

- Unconditional numerical stability in sequential deconvolution is realized.
- Arbitrary (unknown) initial conditions are considered without approximation.
- Observability and controllability are shown immaterial in the reconstruction problem.
- Identifiability is shown determined by the transmission zeros of the input-output map.

A scheme for sequential deconvolution of inputs from measured outputs is presented. The key feature in the formulation is elimination of the initial state from the input-output relations by projecting the output in the left null space of the observability block. Removal of the initial state allows the sequential format of the deconvolution, essential for computational reasons, to be implemented non-recursively, assuring unconditional stability. Identifiability is realized when the input-output arrangement does not have transmission zeros, and observability and controllability are shown immaterial. Comparison of results from the scheme with those from Dynamic Programming highlights the benefits of eliminating the initial state.