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Stabilization of stochastic coupled systems with Markovian switching via feedback control based on discrete‐time state observations
Author(s) -
Wu Yongbao,
Yan Shihan,
Fan Meng,
Li Wenxue
Publication year - 2017
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.3867
Subject(s) - control theory (sociology) , discrete time and continuous time , lyapunov function , stability (learning theory) , state (computer science) , markov process , controller (irrigation) , upper and lower bounds , mathematics , full state feedback , computer science , control (management) , nonlinear system , algorithm , physics , mathematical analysis , statistics , quantum mechanics , artificial intelligence , machine learning , agronomy , biology
Summary This study investigates the stabilization issue of stochastic coupled systems with Markovian switching via feedback control. A state feedback controller based on the discrete‐time observations is applied for the stabilization purpose. By making use of the graph theory and the Lyapunov method, we establish both Lyapunov‐ and coefficient‐type sufficient criteria to guarantee the stabilization in the sense of H ∞ stability, and then, we further develop the mean‐square asymptotical stability. In particular, the upper bound of the duration between 2 consecutive state observations is well formulated. Applications to a concrete stabilization problem of stochastic coupled oscillators with Markovian switching and some numerical analyses are presented to illustrate and to demonstrate the easy verifiability, effectivity, and efficiency of our theoretical findings.