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RANDOMIZED ALGORITHMS FOR STABILIZING SWITCHING SIGNALS

Balachandran, Niranjan and Kundu, Atreyee and Chatterjee, Debasish (2019) RANDOMIZED ALGORITHMS FOR STABILIZING SWITCHING SIGNALS. In: MATHEMATICAL CONTROL AND RELATED FIELDS, 9 (1). pp. 159-174.

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Official URL: https://doi.org/10.3934/mcrf.2019009

Abstract

Qualitative behaviour of switched systems has attracted considerable research attention in the recent past. In this article we study `how likely' is it for a family of systems to admit stabilizing switching signals. A weighted digraph is associated to a switched system in a natural fashion, and the switching signal is expressed as an infinite walk on this digraph. We provide a linear time probabilistic algorithm to find cycles on this digraph that have a desirable property (we call it ``contractivity''), and under mild statistical hypotheses on the connectivity and weights of the digraph, demonstrate that there exist uncountably many stabilizing switching signals derived from such cycles. Our algorithm does not require the vertex and edge weights to be stored in memory prior to its application, has a learning/exploratory character, and naturally fits very large scale systems.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to AMER INST MATHEMATICAL SCIENCES-AIMS
Keywords: Randomized algorithms; discrete-time switched systems; Azuma's inequality
Department/Centre: Division of Electrical Sciences > Electrical Engineering
Depositing User: Id for Latest eprints
Date Deposited: 28 Jan 2019 10:24
Last Modified: 28 Jan 2019 10:24
URI: http://eprints.iisc.ac.in/id/eprint/61518

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