H∞H∞ filtering for nonuniformly sampled systems: A Markovian jump systems approach

This paper is concerned with the design of an H∞H∞ filter for a sampled-data system, where the measurement is sampled nonuniformly and randomly but the input is updated uniformly at a fast rate. The process of nonuniform measurement sampling is modeled using a Markov chain; therefore, the discrete-time system together with the Markov chain is a Markovian jump system. A mode-dependent, full-order H∞H∞ filter is constructed. Sufficient LMI conditions are derived to ensure stochastic stability and H∞H∞ disturbance attenuation for the error system. The case of unknown measurement sampling probabilities is also considered. Finally, the effectiveness of the proposed approach is demonstrated through simulation results and a comparison with a general time-varying H∞H∞ filter.