## Abstract

In this paper, we investigate a problem of exponential state estimation for Markovian jumping genetic regulatory networks with mode-dependent probabilistic time-varying delays. A new type of mode-dependent probabilistic leakage time-varying delay is considered. Given the probability distribution of the time-delays, stochastic variables that satisfying Bernoulli random binary distribution are formulated to produce a new system which includes the information of the probability distribution. Under these circumstances, the state estimator is designed to estimate the true concentration of the mRNA and the protein of the GRNs. Based on Lyapunov-Krasovskii functional that includes new triple integral terms and decomposed integral intervals, delay-distribution-dependent exponential stability criteria are obtained in terms of linear matrix inequalities. Finally, a numerical example is provided to show the usefulness and effectiveness of the obtained results.

Original language | English |
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Pages (from-to) | 30-53 |

Number of pages | 24 |

Journal | Mathematical Biosciences |

Volume | 251 |

Issue number | 1 |

DOIs | |

Publication status | Published - May 2014 |

## Keywords

- Bernoulli distribution
- Genetic regulatory networks
- Global exponential stability
- Linear matrix inequalities
- Mode-dependent time-varying delays

## ASJC Scopus subject areas

- Statistics and Probability
- Modelling and Simulation
- General Biochemistry,Genetics and Molecular Biology
- General Immunology and Microbiology
- General Agricultural and Biological Sciences
- Applied Mathematics