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

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), 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 u₂(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.