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New results on stability and L ∞ ‐gain analysis for positive linear differential‐algebraic equations with unbounded time‐varying delays
Author(s) -
Huu Sau Nguyen,
Viet Thuan Mai
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.4907
Subject(s) - mathematics , algebraic number , monotonic function , bounding overwatch , differential algebraic equation , stability (learning theory) , trajectory , differential equation , differential (mechanical device) , exponential stability , state (computer science) , function (biology) , positive systems , algebraic equation , linear system , mathematical analysis , nonlinear system , computer science , ordinary differential equation , physics , algorithm , thermodynamics , artificial intelligence , machine learning , astronomy , quantum mechanics , evolutionary biology , biology
Summary This article addresses the problems of stability and L ∞ ‐gain analysis for positive linear differential‐algebraic equations with unbounded time‐varying delays for the first time. First, we consider the stability problem of a class of positive linear differential‐algebraic equations with unbounded time‐varying delays. A new method, which is based on the upper bounding of the state vector by a decreasing function, is presented to analyze the stability of the system. Then, by investigating the monotonicity of state trajectory, the L ∞ ‐gain for differential‐algebraic systems with unbounded time‐varying delay is characterized. It is shown that the L ∞ ‐gain for differential‐algebraic systems with unbounded time‐varying delay is also independent of the delays and fully determined by the system matrices. Two numerical examples are given to illustrate the obtained results.