H∞ filtering for non-linear stochastic markovian jump systems

This study deals with the H_∞ filtering problem for a class of non-linear stochastic Markovian jump systems (NSMJS) as to both accessible and non-accessible jumping parameters cases. For this class of systems with measurable Markovian jumping parameters, sufficient conditions are expressed for the non-linear stochastic H_∞ and mixed H₂/H_∞ filtering design in terms of a set of N-, 2N-coupled Hamilton-Jacobi inequalities (HJIs), respectively. On the other hand, as to the non-accessible jumping parameters case, a fault-tolerant H_∞ filter is introduced for NSMJS with a jump detection and identification scheme, which is determined by a set of N×M-coupled HJIs. Finally, a numerical example is given to show the usefulness of the results derived.