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Open‐loop control of parameter‐dependent discrete‐time systems
Author(s) -
Scherlein Barbara,
Schönlein Michael,
Helmke Uwe
Publication year - 2014
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201410450
Subject(s) - eigenvalues and eigenvectors , control theory (sociology) , discrete time and continuous time , mathematics , sequence (biology) , interval (graph theory) , matrix (chemical analysis) , lti system theory , invariant (physics) , linear system , topology (electrical circuits) , computer science , control (management) , mathematical analysis , physics , combinatorics , artificial intelligence , mathematical physics , statistics , materials science , quantum mechanics , biology , composite material , genetics
We consider parameter‐dependent linear time‐invariant discrete‐time single input systems, where the system matrix and the input vector are assumed to depend continuously on a parameter varying over a compact interval. We face the problem of steering the zero state simultaneously arbitrarily close towards a given continuous family of desired terminal states with a finite parameter independent open‐loop input sequence. Starting from existing sufficient conditions, which include simplicity of the eigenvalues of the system matrices, we examine the case of multiple eigenvalues. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)