Stability Analysis And Observer Design Of Delayed Gene Regulating Network

This thesis focuses on stability analysis and designing one state observer for genetic regulatory networks (GRNs) with interval time-varying delays.An improved integral inequality concerning on double-integral items is first established. It is proven that this integral inequality is less conservative than one in literature. This integral inequality will be used to analyze stability and design state observer for GRNs with interval time-varying delays.Then, the problems of stability analysis and designing state observer have been investigated for delayed GRNs. In the research of stability, a pair of delay-dependent asymptotical stability criteria have been constructed in the form of linear matrix inequalities (LMIs) by employing an Lyapunov-Krasovskii functional. Furthermore, it is theoretical and experimental proven that the stability criterion proposed here is less conservative than the corresponding one in [Neurocomputing,2012,93:19-26]. Based on the stability criteria given out previously, we also investigate the robust asymptotical stability conditions for the uncertain GRNs with with interval time-varying delays. In the research of designing an state observer, we obtain a state observer for the certain GRNs by solving the asymptotical stability criterion of the error system.The effectiveness of our approach is illustrated by numerical examples and their simulation results.