Global asymptotic stability of a class of complex networks via decentralised static output feedback control

This study deals with the problem of the decentralised static output feedback for a class of dynamic networks with each node being a general Lur'e system. On the basis of the Kalman'Yakubovich'Popov (KYP) lemma, linear matrix inequality (LMI) conditions guaranteeing the stability of such dynamic networks are established. In addition, the following interesting result is derived: the stability problem for the whole Nn-dimensional dynamic networks can be converted into the simple n-dimensional space in terms of only two LMIs. Finally, a concrete application to mutually coupled phase-locked loop networks shows the validity of the proposed approaches.