Inverse filtering and deconvolution (Q2710029)

For both continuous- and discrete-time linear systems, the subject of inverse filtering or deconvolution is studied. In the first phase of the work, the plant dynamics is assumed to be completely known and the notions of exact, almost, optimal and suboptimal deconvolution problems in the presence of disturbances are introduced and their solvability conditions are formulated. Also the counterparts of these problems when an \(l\)-step delay in estimation is present are introduced and studied. All these problems are highly interconnected and thus form a hierarchical order from a problem that imposes strongest conditions for its solvability to a problem that imposes weakest conditions. In the second part the authors consider uncertain plants where the uncertainties in plant dynamics can be structurally modeled by a \(\Delta\)-block as a feedback element to the nominally known plant dynamics. Two problems, namely exact and almost deconvolution problems, are then studied either in the presence or absence of external disturbances.