Asynchronous l2 − l∞ filtering for Markov jump systems

This study considers the design of l₂ - l_∞ filters for Markov jump systems under asynchronous switching. The asynchronous behavior described by a stochastic variable is considered to be random mismatch between system modes and candidate filters. The jumping process of the filtering error system is modeled as a two component Markov chain. Using a stochastic parameter-dependent approach, sufficient conditions for the addressed filtering problem are obtained. By solving the proposed conditions, a desired l₂ - l_∞ filter can be constructed for any admissible random mismatch. Moreover, a key relationship of l₂ - l_∞ performance between the presented results and the classical mode-dependent, mode-independent filtering is demonstrated. A numerical example is provided to illustrate the validity and potential of the developed method.