Paper:

# Robust Stability of Discrete-Time Randomly Switched Delayed Genetic Regulatory Networks with Known Sojourn Probabilities

## Xiongbo Wan, Chuanyu Ren, and Jianqi An

School of Automation, China University of Geosciences

Wuhan 430074, China

This study investigates stability problems related to discrete-time randomly switched genetic regulatory networks (GRNs) with time-varying delays. A new discrete-time randomly switched GRN model with known sojourn probabilities is proposed. By utilizing the discrete Wirtinger-based inequality and a newly proposed constraint condition on the feedback regulatory function, which have not been fully used in stability analysis of discrete-time GRNs, we establish delay-dependent stability and robust stability criteria. These criteria possess the sojourn probabilities of randomly switched GRNs. Two numerical examples are provided to demonstrate the effectiveness of the established results.

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.20, No.7, pp. 1094-1102, 2016.

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