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Observer‐based H ∞ control on nonhomogeneous Markov jump systems with nonlinear input
Author(s) -
Yin Yanyan,
Shi Peng,
Liu Fei,
Teo Kok Lay
Publication year - 2013
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.2974
Subject(s) - control theory (sociology) , nonlinear system , lyapunov function , observer (physics) , mathematics , polytope , markov chain , jump , discrete time and continuous time , controller (irrigation) , computer science , control (management) , statistics , physics , quantum mechanics , artificial intelligence , discrete mathematics , agronomy , biology
SUMMARY This paper considers the problem of observer‐based H ∞ controller design for a class of discrete‐time nonhomogeneous Markov jump systems with nonlinear input. Actuator saturation is considered to be a nonlinear input of such system and the time‐varying transition probability matrix in the system is described as a polytope set. Furthermore, a mode‐dependent and parameter‐dependent Lyapunov function is investigated, and a sufficient condition is derived to design observer‐based controllers such that the resulting error dynamical system is stochastically stable and a prescribed H ∞ performance is achieved. Finally, estimation of attraction domain of such nonhomogeneous Markov jump systems is also made. A simulation example shows the effectiveness of developed techniques. Copyright © 2013 John Wiley & Sons, Ltd.