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.