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Guaranteed cost control of synchronisation for uncertain complex delayed networks. (English) Zbl 1259.93088

Summary: The synchronisation for a class of complex delayed dynamical networks with uncertain inner coupling configuration is investigated under the quadratic guaranteed cost control. The coupling delay and nodes delay are considered in the networks. Based on Lyapunov–Krasovskii stability theory, sufficient conditions for the existence of the optimal guaranteed cost control laws are given in terms of linear matrix inequalities. Under these sufficient conditions, the networks are globally asymptotically synchronous, and the optimal upper bound is also guaranteed. Numerical examples are given to illustrate the effectiveness of the proposed methods.

MSC:

93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
49N90 Applications of optimal control and differential games
93C15 Control/observation systems governed by ordinary differential equations
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