Mean Square Stabilizability of Hidden Jump Linear Periodic Systems

This paper presents stability and stabilizability criteria for a class of Markov jump linear (MJL) periodic systems under the assumptions of perfect and imperfect mode information. We consider MJL systems with mode-frozen periodic parameters and extend known stability results from MJL systems via a mode augmentation approach. The novel approach is first applied to the case of instantaneous and correct mode information. It is then applied to the case where the mode is hidden yet detected with known probabilities of correct and missed detection. The validity of the suggested criteria is illustrated via simple numerical examples.