An improved stability criterion for linear systems with multi-rate sampled data
type: Item
instance of: scholarly article
title: An improved stability criterion for linear systems with multi-rate sampled data
zbMATH Open document ID: 1485.93470
author: JunMin Park
author: Poogyeon Park
published in: Nonlinear Analysis. Hybrid Systems
publication date: 2021-12-13T00:00:00Z
review text: This paper proposes a stability criterion for linear systems with multi-rate sampled data by constructing novel Lyapunov functionals. The systems are represented as linear systems with input delay. The Lyapunov functionals consist of a quadratic function, an integral term related to the sampling intervals of each sensor and looped-functionals related to the sampling intervals of whole systems. In the view of the Lyapunov stability theorem, the quadratic function and the integral term require the positivity condition, whereas the looped-functionals do not require the positivity condition because the functionals are zeros at the sampling instants. Furthermore, the looped-functionals exploit the information on the sampled state and the state at the next sampling instants. Based on the Lyapunov functionals, this paper derives a stability criterion in terms of linear matrix inequalities. The simulation results show the effectiveness of the proposed stability criterion. This paper considers stability and stabilization problems for linear systems with multi-rate sampled data under aperiodic samplings which are represented as linear systems with an input time delay. To handle the stability problem, the authors construct a Lyapunov functional which consists of a quadratic function, an integral term related to the sampling intervals of each sensor, and looped-functionals related to the sampling intervals of whole systems. The Lyapunov functionals handle the sampling intervals in the view of each sensor and whole systems in the integral term and the looped-functionals, respectively. In the view of the stability theorem, the quadratic function and the integral term require the positivity condition, whereas the looped-functionals do not require the positivity condition because the functionals are zeros at the sampling instants. The looped-functionals utilize the information not only on the interval between the last sampling instant and the present time but also on the interval b…
reviewed by: Nataliya O. Sedova
Mathematics Subject Classification ID: 93D20
Mathematics Subject Classification ID: 93C57
Mathematics Subject Classification ID: 93C23
Mathematics Subject Classification ID: 34K06
Mathematics Subject Classification ID: 93C05
zbMATH DE Number: 7443507
zbMATH Keywords: sampled-data control
zbMATH Keywords: multi-rate samplings
zbMATH Keywords: looped-functional
zbMATH Keywords: linear matrix inequality
MaRDI profile type: Publication
full work available at URL: j.nahs.2020.100947
OpenAlex ID: W3049191684
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DOI: 10.1016/J.NAHS.2020.100947
description: scientific article; zbMATH DE number 7443507