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Stability and stabilization for singularly perturbed systems with Markovian jumps
Author(s) -
Wang Guoliang,
Xu Lei
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.5014
Subject(s) - control theory (sociology) , stability (learning theory) , lyapunov function , controller (irrigation) , upper and lower bounds , mathematics , state (computer science) , matrix (chemical analysis) , markov process , exponential stability , function (biology) , computer science , control (management) , mathematical analysis , nonlinear system , physics , algorithm , statistics , materials science , quantum mechanics , machine learning , artificial intelligence , agronomy , composite material , biology , evolutionary biology
Summary This article focuses on the stability and stabilization problems of singularly perturbed jump systems. Here, the singularly perturbed parameter (SPP) is also with Markov switching and satisfies anyϵ i ∈ ( 0 ,ϵ ‾i ] with positive boundϵ ‾ipredefined. First, stability conditions expressed ϵ i ‐free but involving its bound are developed by constructing an ϵ i ‐dependent Lyapunov function. Then, a method for state feedback stabilization controller depending on SPP is proposed, whose conditions are given in terms of linear matrix inequalities. Moreover, some special cases about deterministic SPP are considered too. Finally, two practical examples are used to demonstrate the effectiveness and superiorities of the proposed methods.