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This study addresses the H∞ control design problem systematically for a class of non-linear stochastic active fault-tolerant control systems with Markovian parameters. A sufficient condition for the non-linear stochastic fault-tolerant H∞ control u1(x(t), ηt) is given in terms of a set of coupled Hamilton-Jacobi inequalities (HJIs). Then, a fuzzy-interpolation approach is developed to conquer the difficulty in solving the coupled HJIs, which sustains a fault-tolerant H∞ fuzzy control u2(x(t), ηt) by solving linear matrix inequalities, instead of HJIs. A simulation example is presented to illustrate the effectiveness of the proposed design method.
Date of Publication: October 2010