Switching Controller Design for a Class of Markovian Jump Nonlinear Systems Using Stochastic Small-Gain Theorem

Switching Controller Design for a Class of Markovian Jump Nonlinear Systems Using Stochastic Small-Gain Theorem

Switching controller design for a class of Markovian jump nonlinear systems with unmodeled dynamics is considered in this paper. Based on the differential equation and infinitesimal generator of jump systems, the concept of Jump Input-to-State practical Stability (JISpS) in probability and stochasti...

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Main Authors: Jin Zhu, Junhong Park, Kwan-Soo Lee, Maksym Spiryagin
Format: Article
Language:English
Published: SpringerOpen 2009-01-01
Series:Advances in Difference Equations
Online Access:http://dx.doi.org/10.1155/2009/896218
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spelling doaj-4006a584f5ef4065a4121b36eb68d2b02020-11-24T22:25:47ZengSpringerOpenAdvances in Difference Equations1687-18391687-18472009-01-01200910.1155/2009/896218Switching Controller Design for a Class of Markovian Jump Nonlinear Systems Using Stochastic Small-Gain TheoremJin ZhuJunhong ParkKwan-Soo LeeMaksym SpiryaginSwitching controller design for a class of Markovian jump nonlinear systems with unmodeled dynamics is considered in this paper. Based on the differential equation and infinitesimal generator of jump systems, the concept of Jump Input-to-State practical Stability (JISpS) in probability and stochastic Lyapunov stability criterion are put forward. By using backsetpping technology and stochastic small-gain theorem, a switching controller is proposed which ensures JISpS in probability for the jump nonlinear system. A simulation example illustrates the validity of this design. http://dx.doi.org/10.1155/2009/896218
collection DOAJ
language English
format Article
sources DOAJ
author Jin Zhu
Junhong Park
Kwan-Soo Lee
Maksym Spiryagin
spellingShingle Jin Zhu
Junhong Park
Kwan-Soo Lee
Maksym Spiryagin
Switching Controller Design for a Class of Markovian Jump Nonlinear Systems Using Stochastic Small-Gain Theorem
Advances in Difference Equations
author_facet Jin Zhu
Junhong Park
Kwan-Soo Lee
Maksym Spiryagin
author_sort Jin Zhu
title Switching Controller Design for a Class of Markovian Jump Nonlinear Systems Using Stochastic Small-Gain Theorem
title_short Switching Controller Design for a Class of Markovian Jump Nonlinear Systems Using Stochastic Small-Gain Theorem
title_full Switching Controller Design for a Class of Markovian Jump Nonlinear Systems Using Stochastic Small-Gain Theorem
title_fullStr Switching Controller Design for a Class of Markovian Jump Nonlinear Systems Using Stochastic Small-Gain Theorem
title_full_unstemmed Switching Controller Design for a Class of Markovian Jump Nonlinear Systems Using Stochastic Small-Gain Theorem
title_sort switching controller design for a class of markovian jump nonlinear systems using stochastic small-gain theorem
publisher SpringerOpen
series Advances in Difference Equations
issn 1687-1839
1687-1847
publishDate 2009-01-01
description Switching controller design for a class of Markovian jump nonlinear systems with unmodeled dynamics is considered in this paper. Based on the differential equation and infinitesimal generator of jump systems, the concept of Jump Input-to-State practical Stability (JISpS) in probability and stochastic Lyapunov stability criterion are put forward. By using backsetpping technology and stochastic small-gain theorem, a switching controller is proposed which ensures JISpS in probability for the jump nonlinear system. A simulation example illustrates the validity of this design.
url http://dx.doi.org/10.1155/2009/896218
work_keys_str_mv AT jinzhu switchingcontrollerdesignforaclassofmarkovianjumpnonlinearsystemsusingstochasticsmallgaintheorem
AT junhongpark switchingcontrollerdesignforaclassofmarkovianjumpnonlinearsystemsusingstochasticsmallgaintheorem
AT kwansoolee switchingcontrollerdesignforaclassofmarkovianjumpnonlinearsystemsusingstochasticsmallgaintheorem
AT maksymspiryagin switchingcontrollerdesignforaclassofmarkovianjumpnonlinearsystemsusingstochasticsmallgaintheorem
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