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A Study on Stability Analysis for Complex Dynamical Networks with Time Delays

A Study on Stability Analysis for Complex Dynamical Networks with Time Delays
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This thesis considers stability conditions for networks with time-varying de-lays. In this thesis, sufficient stability conditions of complex dynamical net-works (CDN) and those of genetic regulatory networks (GRN) are derived. Thederived conditions are based on linear matrix inequality (LMI) framework. Thisthesis mainly contributes to make the stability conditions be less conservative.For two different type of CDN, e.g., singular CDN and neutral CDN, syn-chronization problems are considered. First, delay-dependent synchronizationof singular complex dynamical networks with time-varying delays is consid-ered. A modified Lyapunov-Krasovskii functional is used to derive a sufficientcondition for synchronization in terms of LMIs which can be easily solved byvarious convex optimization algorithms. Second, the synchronization problemfor a class of neutral complex dynamical networks with coupling time-varyingdelays is considered. A delay-dependent synchronization criterion is derivedfor the synchronization of neutral complex dynamical networks. By the use of aconvex representation of the sector-restricted nonlinearity in system dynamics,the stability condition based on the discretized Lyapunov-Krasovskii functionalis obtained via LMI formulation.On the other hand, an improved robust delay-dependent stability criteria forgenetic regulatory networks with delays which varies in an interval. Based onLyapunov-Krasovskii functional, a new delay-dependent sufficient conditions in terms of LMIs is derived, which is represented by a convex combination. Thederived stability condition is without free-weighting matrices so that it reducesthe computation burden.All the stability conditions are less conservative than ones in literature. Numericalsimulations are provided to show the effectiveness of the proposedmethod.
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