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Stability analysis of positive switched impulsive systems with delay on time scales
Author(s) -
Lu Xiaodong,
Li Haitao,
Wang Chuankui,
Zhang Xianfu
Publication year - 2020
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.5145
Subject(s) - control theory (sociology) , stability (learning theory) , mathematics , derivative (finance) , discrete time and continuous time , lyapunov function , scale (ratio) , computer science , control (management) , nonlinear system , statistics , machine learning , artificial intelligence , physics , quantum mechanics , financial economics , economics
Summary In this paper, stability analysis of positive switched impulsive systems with delay on time scales is investigated. Firstly, a necessary and sufficient condition is provided for positivity of the considered systems. Secondly, by respectively considering the situations that the switching behavior and the impulsive phenomenon happen simultaneously and asynchronously, the uniformly asymptotical stability problems are addressed. Then, based on the linear copositive Lyapunov‐Krasovskii functional technique, two less conservative stability criteria are proposed. It are shown that these two criteria allow the time‐scale derivative of related Lyapunov functionals to be non‐negative at some intervals. Moreover, these two criteria are effective for not only continuous cases and discrete cases, but also some other positive switched impulsive systems on general uniform or hybrid time domains. Finally, a non‐continuous and non‐discrete example is given to illustrate the effectiveness of the theoretic results.