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Conditions for stabilizability of time‐delay systems with real‐rooted plant
Author(s) -
Balogh Tamas,
Boussaada Islam,
Insperger Tamas,
Niculescu SilviuIulian
Publication year - 2022
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.5698
Subject(s) - mathematics , control theory (sociology) , multiplicity (mathematics) , factorization , lti system theory , controller (irrigation) , inverted pendulum , linear system , mathematical analysis , computer science , control (management) , algorithm , nonlinear system , agronomy , physics , quantum mechanics , artificial intelligence , biology
In this article we consider the γ ‐stabilization of n th‐order linear time‐invariant dynamical systems using multiplicity‐induced‐dominancy ‐based controller design in the presence of delays in the input or the output channels. A sufficient condition is given for the dominancy of a real root with multiplicity at least n + 1 and at least n using an integral factorization of the corresponding characteristic function. A necessary condition for γ ‐stabilizability is analyzed utilizing the property that the derivative of a γ ‐stable quasipolynomial is also γ ‐stable under certain conditions. Sufficient and necessary conditions are given for systems with real‐rooted open‐loop characteristic function: the delay intervals are determined where the conditions for dominancy and γ ‐stabilizability are satisfied. The efficiency of the proposed controller design is shown in the case of a multilink inverted pendulum.