On the Observability of a Linear System With a Sparse Initial State

Joseph, Geethu and Murthy, Chandra R (2018) On the Observability of a Linear System With a Sparse Initial State. In: IEEE SIGNAL PROCESSING LETTERS, 25 (7). pp. 994-998.

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Abstract

In this letter, we address the problem of observability of a linear dynamical system from compressive measurements and the knowledge of its external inputs. Observability of a high dimensional system state may require a large number of measurements in general, but we show that if the initial state vector admits a sparse representation, the number of measurements can be significantly reduced by using random projections for obtaining the measurements. We derive guarantees for the observability of the system using tools from probability theory and compressed sensing. Our analysis uses properties of the transfer matrix and random measurementmatrices to derive concentration ofmeasure bounds, which lead to sufficient conditions for the restricted isometry property of the observability matrix to hold. Hence, under the derived conditions, the initial state can be recovered by solving a computationally tractable convex optimization problem.

Item Type:	Journal Article
Publication:	IEEE SIGNAL PROCESSING LETTERS
Publisher:	Copyright of this article belong to
Additional Information:	Copyright of this article belong to Copyright of this article belong t
Department/Centre:	Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited:	02 Jul 2018 18:23
Last Modified:	02 Jul 2018 18:23
URI:	http://eprints.iisc.ac.in/id/eprint/60117

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