Robust Stability Analysis of gene regulatory networks
|School||Central South University|
|Course||Control Science and Engineering|
|Keywords||Gene regulatory networks Time-varying delay Random interference Stability Improved free - weighting matrix method|
With the development of bioinformatics , gene regulatory network model to study the interaction between genes and proteins , understanding the inner mechanisms of the biological systems is a research focus . Gene regulatory networks is the bio-dynamic system , its basic characteristics of stability , has important significance . In this paper, we consider the non-linearity of gene regulatory networks , delay, random interference characteristics , the establishment has the Lurie system in the form of continuous-time gene regulatory networks . At the same time , the semi-discrete processing , discrete-time differential equation model with time-varying delay differential equation model . Variable Delays and random noise in gene regulatory networks of continuous-time model for a range , the use of new augmented Lyapunov - Krasovskii Pan letter , considering the delay , delay upper and lower bounds and poor interaction between , citing improved free weight matrix method and basic inequality the functional weak reserved infinity considered useful in the sub- items / delay rate of change proposed a less conservative delay-dependent stability conditions are related . On this basis , uses the mathematics related lemma and introduction of adjustable parameters , to reduce the number of decision variables , thereby reducing the computational complexity of the stability condition . Get delay / delay is independent of the rate of change of delay-independent stability condition , and the results are extended to the case with time-varying structured uncertainties . Given numerical example illustrates the effectiveness of the method and compared with existing results superiority . Augmented Lyapunov - Krasovskii functional discrete-time model with interval varying Delay and random noise , combined with improved free - weighting matrix method is proposed the related delay / delay range of the global asymptotic stability conditions , at the same time explore the delay independent stability conditions . Consider the model parameter uncertainty , robust stability conditions . Given numerical example illustrates the effectiveness of the method . Finally, a summary of the stability studies of gene regulatory networks , and future research direction .