Mean square exponential and robust stability of stochastic discrete-time genetic regulatory networks with uncertainties

Abstract

This paper aims to analyze global robust exponential stability in the mean square sense of stochastic discrete-time genetic regulatory networks with stochastic delays and parameter uncertainties. Comparing to the previous research works, time-varying delays are assumed to be stochastic whose variation ranges and probability distributions of the time-varying delays are explored. Based on the stochastic analysis approach and some analysis techniques, several sufficient criteria for the global robust exponential stability in the mean square sense of the networks are derived. Moreover, two numerical examples are presented to show the effectiveness of the obtained results.

Kalman Filtering for Genetic Regulatory Networks with Missing Values

“…Clearly, a discrete-time model of genetic regulatory networks (GRNs) can be described as follows [ 21 – 23 ]: where the descriptions of system's parameters are shown in Table 1 .…”

New Stability Criterion for Discrete-Time Genetic Regulatory Networks with Time-Varying Delays and Stochastic Disturbances

“…Up to now, there is a little work on the discrete-time GRNs with delays [20][21][22][23]. Recently, the asymptotic stability problem has been investigated in [24] for a class of discrete-time uncertain stochastic GRNs with time-varying delays, where a set of sufficient conditions to ensure the stability has been derived in terms of LMIs, while the exponential stability analysis and the robust ∞ control problems for discrete-time GRNs have been investigated in [25,26]. On the other hand, it is well recognized that the noise, which involves the intrinsic fluctuation and extrinsic noise, may impose great effect on system performance of the complex systems [27][28][29][30][31].…”

H∞Filtering for Discrete-Time Genetic Regulatory Networks with Random Delay Described by a Markovian Chain

“…It should also be emphasized that for delayed discretetime GRNs, the stability problem (as the most important properties for any dynamics systems) [27][28][29], ∞ stabilization problem [30], and passivity problem [31] have been exploited. On the other hand, researchers have been paying attention to the problems of analysis and synthesis for Markovian jump system [32][33][34][35][36] and the filtering problems for some nonlinear systems [37][38][39][40][41].…”