Delay-dependent passivity analysis of nondeterministic genetic regulatory networks with leakage and distributed delays against impulsive perturbations

Abstract

This work is concerned with the problem for stochastic genetic regulatory networks (GRNs) subject to mixed time delays via passivity control in which mixed time delays consist of leakage, discrete, and distributed delays. The main aim of this paper is constructing a passivity-based criteria under impulsive perturbations such that the proposed GRNs are stochastically stable. Based on the Lyapunov functional method and Jensen’s integral inequality, we obtain a new set of novel passivity based delay-dependent sufficient condition in the form of LMIs, which can be determined via existing numerical software. Finally, we propose numerical simulations to show the efficiency of the proposed method.

H∞ controller design for singular Markov jump systems with time-delays

“…The research of Markov jump system originated in the 1960s. In recent years, with the rapid development of computer technology and the continuous improvement of mathematical theory, the analysis and design of Markov jump system have attracted extensive attention of scholars, 1–3 such as dissipative control problem, 4–6 adaptive control problem, 7,8 fault tolerant control problem, 9 fault detection problem, 10 and H ∞ filtering problem. 11,12…”

State bounding and controller design for genetic regulatory networks with multiple delays and bounded disturbances

“…Wang et al 14 investigated robust $$$ {H}_{\infty } $$$ filtering problem for uncertain stochastic GRNs with mixed time‐varying delays. The passivity of stochastic GRNs with leakage and distributed delays against impulsive perturbations had been addressed in Reference 15. The region that the states of GRNs with multiple delays and disturbances can reach when the states start from a certain area is a matter of concern in practical engineering.…”