Adaptive synchronization of a network of interconnected nonlinear Lur'e systems

The problem of adaptive synchronization is formulated for networks of interconnected dynamical subsystems containing a leading subsystem. Considered are networks of subsystems specified in the Lur'e form (a linear part plus nonlinearity) of the following three types: Subsystems containing Lipschitz nonlinearities, those with non-Lipschitz nonlinearities in a certain class, and networks with structural matching between the leading subsystem and the driven ones. Decentralized algorithms of adaptive control are synthesized using the speed gradient method. The conditions of synchronizability are obtained through use of the method of passification and the Yakubovich–Kalman lemma. In contrast to the existing results, the case of incomplete measurements is considered along with the situation where the control input may not affect the equations of all subsystems. The results are exemplified by applications to Chua's circuits.