Stability analysis of a class of nonlinear positive switched systems with delays. (May 2015)

• Record Type: Journal Article
• Authors: Liu, Xingwen
• Is Part Of: Nonlinear analysis. Volume 16(2015)
• Page Start: 1
• Page End: 12
• Publication Date: 2015-05
• Subjects: Delays -- Nonlinear systems -- Positive systems -- Stability -- Switched systems; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2014.12.002
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: This paper addresses the stability problem of delayed nonlinear positive switched systems whose subsystems are all positive. Both discrete-time systems and continuous-time systems are studied. In our analysis, the delays in systems can be unbounded. Two conditions are established to test the local asymptotic stability of the considered systems. The method to compute the domains of attraction is also proposed provided that the system is locally asymptotically stable. When reduced to general nonlinear positive systems, that is, the considered switched system consists of only one mode, an interesting conclusion follows that the proposed nonlinear positive system is locally asymptotically stable for all admissible delays and nonnegative nonlinearities which satisfy an extra condition at the origin, if and only if the system represented by the linear part is asymptotically stable for all admissible delays. Finally, a numerical example is presented to illustrate the obtained results.