${H}_{\infty }$ Filtering for Fuzzy Jumping Genetic Regulatory Networks With Round-Robin Protocol: A Hidden-Markov-Model-Based Approach

Abstract

In this article, a method to design the filter for fuzzy jumping genetic regulatory networks is explored. The case when the filters cannot directly utilize the mode information of the plant is taken into account. A hidden Markov model is introduced to address such a problem. Furthermore, a mature scheduling method, namely round-robin protocol, is employed to optimize the data transmission in genetic regulatory networks. On the basis of the fuzzy model approach and the stochastic analysis technique, some novel conditions ensuring the $H_{\infty }$ performance and stochastic stability of the error system are established. The parameters of the filter can be presented via addressing the convex optimization problem. The feasibility of results is finally illustrated by considering a repressilator model subject to stochastic jumping parameters.