H∞ stabilisation of non-linear stochastic active fault-tolerant control systems: fuzzy-interpolation approach

Abstract

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 u 1 (x(t), η t ) 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 u 2 (x(t), η t ) by solving linear matrix inequalities, instead of HJIs. A simulation example is presented to illustrate the effectiveness of the proposed design method.