Abstract / truncated to 115 words (read the full abstract)

This thesis develops new mathematical theory and presents novel recovery algorithms for discrete linear dynamical systems (LDS) with sparsity constraints on either control inputs or initial state. The recovery problems in this framework manifest as the problem of reconstructing one or more sparse signals from a set of noisy underdetermined linear measurements. The goal of our work is to design algorithms for sparse signal recovery which can exploit the underlying structure in the measurement matrix and the unknown sparse vectors, and to analyze the impact of these structures on the efficacy of the recovery. We answer three fundamental and interconnected questions on sparse signal recovery problems that arise in the context of LDS. First, what ... toggle 14 keywords

linear dynamical systems – sparsity – observability – compressed sensing – sparse signal recovery – controllability – kalman rank test – pbh test – switched linear systems – kalman filter – multiple measurement vectors – sparse representation – dictionary learning – nonconvex optimization.

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