## Guaranteed cost synchronization of a complex dynamical network via dynamic feedback control.(English)Zbl 1238.93070

Summary: In this paper, the problem of guaranteed cost synchronization for a complex network is investigated. In order to achieve the synchronization, two types of guaranteed cost dynamic feedback controllers are designed. Based on Lyapunov’s stability theory, a Linear Matrix Inequality (LMI) convex optimization problem is formulated to find the controller which guarantees the asymptotic stability and minimizes the upper bound of a given quadratic cost function. Finally, a numerical example is given to illustrate the proposed method.

### MSC:

 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory 93D20 Asymptotic stability in control theory 93B52 Feedback control 90C22 Semidefinite programming
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