Paper Info
Title
Positivity and Stability Analysis for Fractional-Order Delayed Systems: A T-S Fuzzy Model Approach
Abstract
This article investigates positivity, external positivity, and asymptotic stability for a large class of incommensurate fractional-order nonlinear systems (FONSs) with bounded multiple time-varying delays by virtue of the T-S fuzzy method. The Laplace transformation technique is used to obtain the solutions of T-S fuzzy FONSs. A sufficient and necessary condition is derived for characterizing (internal) positivity, and certain criteria are also provided to guarantee external positivity of FONSs with or without time-varying delays. It is indicated that the positivity of the considered systems is determined purely by system matrices rather than the magnitudes of time-varying delays. Moreover, a sufficient and necessary condition for asymptotic stability of positive FONSs is obtained, and a state-feedback controller is also designed to guarantee that state variables not only converge to the origin asymptotically but also remain nonnegative, where the control gain matrix is obtained by solving an linear programming (LP) problem. Three numerical simulation examples are given to expound validity and feasibility of the theoretical results.
Year
DOI
Venue
2021
10.1109/TFUZZ.2020.2966420
IEEE Transactions on Fuzzy Systems
Keywords
DocType
Volume
Asymptotic stability,fractional-order system,positivity,time-varying delay,T-S fuzzy model
Journal
29
Issue
ISSN
Citations 
4
1063-6706
3
PageRank 
References 
Authors
0.37
10
5
Name
Order
Citations
PageRank
Heng Liu115327.10
Yongping Pan21013.86
Jinde Cao311399733.03
Y. Zhou416337.69
Hongxing Wang5162.66