Extended _∞ estimation for two-dimensional Markov jump systems under asynchronous switching

This paper is concerned with the problem of designing _∞ filters for a class of two-dimensional (2D) Markov jump systems under asynchronous switching. The problem under consideration is primarily motivated by a realistic situation that the switching of candidate filters may have a lag to the switching of system modes. Different from conventional techniques, by a suitable augmentation, the jumping process of the error system is represented by a two-component Markov chain. Then, the extended transition probabilities are provided for the error system. A stochastic Lyapunov function approach is proposed for the design of desired filters that ensure a prescribed _∞ performance for admissible asynchronous switching. Finally, a numerical example is given to illustrate the effectiveness of the developed method.