Conditions for stabilizability of time-delay systems with real-rooted plant

Tamas Balogh (1) , Islam Boussaada (2, 3, 4) , Tamas Insperger (1) , Silviu-Iulian Niculescu (2, 4)

1 BME - Budapest University of Technology and Economics [Budapest]
2 L2S - Laboratoire des signaux et systèmes
3 IPSA - Institut Polytechnique des Sciences Avancées
4 DISCO - Dynamical Interconnected Systems in COmplex Environments

In this paper we consider the-stabilization of th-order linear time-invariant (LTI) dynamical systems using Multiplicity-Induced-Dominancy (MID)-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 using an integral factorization of the corresponding characteristic function. A necessary condition for-stabilizability is analyzed utilizing the property that the derivative of \alpha-stable quasipolynomial is also-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 \alpha-stabilizability are satisfied. The efficiency of the proposed controller design is shown in the case of a multi-link inverted pendulum.

Mots clés: feedback system; time delay; stabilizability; characteristic equation; dominant roots

Domaines: Automatique / Robotique; Systèmes dynamiques [math.DS]

Tamas Balogh, Islam Boussaada, Tamas Insperger, Silviu-Iulian Niculescu. Conditions for stabilizability of time-delay systems with real-rooted plant. International Journal of Robust and Nonlinear Control, 2021, ⟨10.1002/rnc.5698⟩. ⟨hal-03277678⟩