Random Gene Regulatory Networks With Time-varying Delay Modeling And H_ Up Control Research

With the development of computing science and information technology, genetic regulatory networks (GRNs) have received considerable attention and remarkable progress has been made in the past several decades, which does a great favor for exploration to bio-mechanism and causes of the disease, drug design, etc. Hence, the research on GRNs’structure and dynamic mechanism is of important theoretical significance and application value, and has been one of the most challenging frontier topics in the fields of life information science and biomedicine.By means of nonlinear stochastic theory and technique of computer simulation, this thesis centres on the modeling and controller design for GRNs by considering the effects from time-varying delays, stochastic perturbation, nonlinear interaction and parameter uncertaintiues. The main works are as follows:Firstly, based on deep analysis in biological mechanismthis of GRNs, intrinsic perturbation caused by inherent physical-chemical reaction is supposed to be stochastic process dependent on the states in this thesis. Then a kind of stochastic differential equation model reflecting more real GRNs better is established under full consideration of inevitable factors, including external noises, time-varying delays, structured uncertainties and nonlinear effects.Secondly, for nominal GRNS with time-varying delays and stochastic perturbation, on the basis of the Lyapunov stability theory, taking the relationship among the time-varying delay into account, its upper (lower) bound, and their difference, delay-dependent bounded real conditions are derived via employing an improved free-weighting matrix approach. Besides, the skills of inequality transformations are adopted to transform Hx controllers design problem into linear matrix inequality (LMI) solving problem, and thus an effective method of memoryless state-feedback control for GRNs is proposed. The results are then extended to analyze the delay-dependent stability for GRNs. Finally, for uncertain GRNS with time-varying delays and stochastic perturbation, an appropriate Lyapunov-Krasovskii functional candidate is chosen firstly. Combining the free-weighting matrix approach, robust stabilization analysis and robust Hx control problem for GRNs are discussed by introducing the improved skills of inequality transformations and the cone complementarity liberalization (CCL), respectively. Two corresponding feasible methods of memory state-feedback robust stabilizing controllers and robust Hx controllers design for GRNs are presented.