High-Order Moment Filtering for Markov Jump Systems in Finite Frequency Domain

Considering that state distribution obeys a generalized Gaussian distribution, it cannot be accurately estimated using only the mean error criterion or mean square error criterion. Therefore, this brief addresses the high-order moment filter design problem for Markov jump systems in the finite frequency domain. An estimation method is applied by transforming the original stochastic system into a high-order component form via the cumulant generating function. Then, the generalized Kalman-Yakubovic-Popov lemma can be used in filter design, by considering finite frequency characteristics. Sufficient conditions for the existence of a high-order moment filter with the required finite frequency performance are established. Finally, a simulation example is presented to verify the effectiveness of the proposed method.