Title :
Stability analysis of genetic regulatory network with time delays and parameter uncertainties
Author :
Wang, Zhen ; Liao, Xiaofeng ; Guo, Sini ; Liu, Guo-Ping
Author_Institution :
Coll. of Inf. Sci. & Eng., Chongqing Jiaotong Univ., Chongqing, China
fDate :
10/1/2010 12:00:00 AM
Abstract :
The effect of parameter uncertainties on stability of delayed genetic regulatory networks is investigated. With the presence of parameter uncertainties, the delayed coupled genetic regulatory network is a parameter-dependent non-linear system, in which not only the dynamics are indefinite but also its equilibrium point is unknown. The authors first derive a sufficient condition to guarantee robust stability of uncertain genetic regulatory networks by introducing convergence region. Then, the estimation of convergence region bound is obtained by using Lyapunov stability theory and linear matrix inequality. It is worth noting that these results are derived in the case that the equilibrium point of parameter-dependent non-linear system is unknown. Finally, two examples are given to illustrate the effectiveness of the proposed results.
Keywords :
Lyapunov methods; biology; convergence; delays; genetic engineering; linear matrix inequalities; nonlinear control systems; robust control; stability; Lyapunov stability theory; convergence region; equilibrium point; genetic regulatory network; linear matrix inequality; parameter uncertainties; parameter-dependent nonlinear system; robust stability; stability analysis; time delays;
Journal_Title :
Control Theory & Applications, IET
DOI :
10.1049/iet-cta.2010.0004