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IMA Journal of Mathematical Control and Information 2000 17(3):295-308; doi:10.1093/imamci/17.3.295
© 2000 by Institute of Mathematics and its Applications
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Robust H{infty} control for Markovian jump nonlinear systems

M. D. S. ALIYU1 and E. K. BOUKAS2 {dagger}

1Systems Engineering Department, King Fahd University of Petroleum and Minerals Dhahran 31261, Saudi Arabia
2Mechanical Engineering Department, École Polytechnique de Montréal P.O. Box 6079, station ‘Center-ville’, Montréal, Québec, Canada H3C 3A7

This paper deals with the robust H{infty} control problem of uncertain nonlinear stochastic systems with Markovian jump parameters. We assume that the uncertainties are structured such that suitable bounding functions can be found. A robust controller is then designed that will guarantee disturbance attenuation and asymptotic stability for all admissible uncertainties and L2-bounded disturbances. The solution to the problem is characterized in terms of a set of smooth-positive semidefinite functions satisfying certain Hamilton-Jacobi-Isaac (HJI) inequalities with some appropriate scaling functions. Both the case of matched and unmatched uncertainties are considered.

Keywords: nonlinear system; Markov jump process; dissipative system; disturbance attenuation; matching conditions.

{dagger} Email: boukas{at}anas.meca.polymtl.ca


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