Persistency of excitation criteria for linear, multivariable, time- varying systems
type: Item
instance of: scholarly article
title: Persistency of excitation criteria for linear, multivariable, time- varying systems
zbMATH Open document ID: 0657.93073
DOI: 10.1007/BF02551284
author: S. H. Smith
published in: MCSS. Mathematics of Control, Signals, and Systems
publication date: 1988-01-01T00:00:00Z
review text: Persistency of excitation (PE) and sufficient richness (SR) results are of inportance for convergence studies of adaptive estimation and control schemes. This paper considers both time-invariant and time-varying linear continuous-time systems for which a number of PE and SR results are proved. Specifically: (a) Conditions are derived under which the PE of the output (or state) of a time-invariant MIMO system implies the PE of the output (or state) of another time-invariant MIMO system with the same input and dynamically related to the first; a new definition of SR for vector input signals in terms of a PE condition on a basic regression vector is also given; (b) In the SISO case exact conditions under which the PE of a signal is or is not preserved through dynamical filtering are established; and (c) Conditions are presented under which the output (or state) of a linear time-varying system is PE when its input is SR. These conditions assume that the time variations of the system parameters are either sufficiently slow or integral small.
Mathematics Subject Classification ID: 93E12
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 93C40
Mathematics Subject Classification ID: 93C35
zbMATH DE Number: 4074950
zbMATH Keywords: time-dependent
reviewed by: Petre Stoica
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02551284
OpenAlex ID: W2031607612
description: scientific article; zbMATH DE number 4074950