Conditions for stabilizability of time‐delay systems with real‐rooted plant. (22nd July 2021)

• Record Type: Journal Article
• Authors: Balogh, Tamas; Boussaada, Islam; Insperger, Tamas; Niculescu, Silviu‐Iulian
• Other Names: Mondié Sabine guestEditor.; Egorov Alexey guestEditor.
• Is Part Of: International journal of robust and nonlinear control. Volume 32:Number 6(2022)
• Page Start: 3206
• Page End: 3224
• Publication Date: 2021-07-22
• Subjects: characteristic equation -- dominant roots -- feedback system -- stabilizability -- time delay; Automatic control -- Periodicals; Control theory -- Periodicals; Nonlinear systems -- Periodicals; 629.836
• DOI: 10.1002/rnc.5698
• Languages: English
• ISSNs: 1049-8923

Abstract

Abstract: 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.