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Measurement Bounds for Observability of Linear Dynamical Systems under Sparsity Constraints

Joseph, G and Murthy, CR (2019) Measurement Bounds for Observability of Linear Dynamical Systems under Sparsity Constraints. In: IEEE Transactions on Signal Processing, 67 (8). pp. 1992-2006.

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Official URL: https://dx.doi.org/10.1109/TSP.2019.2899812

Abstract

In this paper, 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 in general requires a correspondingly large number of measurements. 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. Our analysis gives sufficient conditions for the restricted isometry property of the observability matrix to hold, which leads to guarantees for the observability of the system. Our results depend only on the properties of system transfer and observation matrices, and are derived using tools from probability theory and compressed sensing. Unlike the prior work in this direction, our results are applicable to systems with an arbitrary nonzero system transfer matrix. Moreover, our results are stronger than the existing results in the regime where they are comparable.

Item Type: Journal Article
Additional Information: The copyrightfor this article belongs to Institute of Electrical and Electronics Engineers Inc.
Keywords: Compressed sensing; Dynamical systems; Linear control systems; Probability; Signal reconstruction; Transfer matrix method, Compressive measurements; High-dimensional systems; Initial state vectors; Linear dynamical systems; Restricted isometry properties; Sparse representation; Sparse signal recoveries; Sparsity constraints, Observability
Department/Centre: Division of Electrical Sciences > Electrical Communication Engineering
Depositing User: Id for Latest eprints
Date Deposited: 10 Apr 2019 05:55
Last Modified: 10 Apr 2019 05:55
URI: http://eprints.iisc.ac.in/id/eprint/62061

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