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. The
derived conditions are based on linear matrix inequality (LMI) framework. This
thesis 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 synchronization
of singular complex dynamical networks with time-varying delays is consid-
ered. A modified Lyapunov-Krasovskii functional is used to derive a sufficient
condition for synchronization in terms of LMIs which can be easily solved by
various convex optimization algorithms. Second, the synchronization problem
for a class of neutral complex dynamical networks with coupling time-varying
delays is considered. A delay-dependent synchronization criterion is derived
for the synchronization of neutral complex dynamical networks. By the use of a
convex representation of the sector-restricted nonlinearity in system dynamics,
the stability condition based on the discretized Lyapunov-Krasovskii functional
is obtained via LMI formulation.
On the other hand, an improved robust delay-dependent stability criteria for
genetic regulatory networks with delays which varies in an interval. Based on
Lyapunov-Krasovskii functional, a new delay-dependent sufficient conditions in terms of LMIs is derived, which is represented by a convex combination. The
derived stability condition is without free-weighting matrices so that it reduces
the computation burden.
All the stability conditions are less conservative than ones in literature. Numerical
simulations are provided to show the effectiveness of the proposed
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