Detector-based approach for H ∞ filtering of Markov jump linear systems with partial mode information

The goal of this study is to present new results for H ∞ filtering for continuous-time Markov jump linear systems with partial information on the jumping parameter. The central hypothesis considered here is the existence of a suitable detector, which provides measurements of the Markov chain. Besides the interest in its own right, this detector-based approach allows us to treat, in a unified manner, the cases with complete observations, no information and cluster observations of the jumping process as particular scenarios. The main result comprises a method for designing a mean square stable linear H ∞ filter by using the information given by the detector, in the limit case where the sensors respond at much faster rates than the system dynamics. The proposed filter design is given in terms of parameterised linear matrix inequalities (LMIs), which are tackled through an iterative LMI-based algorithm. Furthermore, the result is applied to the state estimation of an unmanned aerial vehicle model.