$${H_\infty }$$ Filtering for Uncertain Periodic Markov Jump Systems with Periodic and Partly Unknown Information

This paper studies the problem of \({H_\infty }\) filtering for a class of uncertain discrete-time periodic Markov jump systems with partly unknown and periodic transition probabilities, which is described as a polytope. By using Lyapunov function, periodic \({H_\infty }\) filter is designed, which ensures that the periodic dynamic system is stochastically stable and satisfies a prescribed \({H_\infty }\) performance index. A numerical example is presented to illustrate the effectiveness of the proposed theoretical results.