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Distinguishability of discrete‐time linear systems
Author(s) -
Silvestre Daniel,
Rosa Paulo,
Silvestre Carlos
Publication year - 2020
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.5367
Subject(s) - constraint (computer aided design) , control theory (sociology) , linear system , discrete time and continuous time , computer science , set (abstract data type) , stability (learning theory) , lti system theory , invariant (physics) , mathematics , upper and lower bounds , mathematical optimization , control (management) , artificial intelligence , mathematical analysis , geometry , machine learning , mathematical physics , programming language , statistics
This article introduces the notion of absolutely distinguishable discrete‐time dynamic systems, with particular applicability to linear time‐invariant and linear parameter‐varying systems. The motivation for this novel type of distinguishability stems, in particular, from the stability and performance requirements of worst‐case adaptive control methodologies. The main results presented herein show that, in most practical cases, a persistence of excitation type of condition and a minimum number of iterations are required to properly distinguish two dynamic systems. We also demonstrate that the former constraint can be written as a lower bound on the intensity of the exogenous disturbances. The applicability of the developed theory is illustrated with a set of examples.