On decentralized hierarchic stabilization of a large-scale system with constraints (Q1099117)

A stabilization method of a large-scale dynamic system, consisting of a set of subsystems with interconnection structure given by a tree network, is considered. With applications in mind, the stabilization of the system is accomplished by using only linear constant state feedback in a completely decentralized way, i.e. with respect to each subsystem individually without taking account of the interconnections existing among the elements. According to the topology of the system, the stabilization method is hierarchical (sequential) and hence easily applicable on a computer. The main result of the paper is the development of a recursive formula for evaluation of the correction multipliers, introduced by \textit{E. J. Davison} [Automatica 10, 309-316 (1974; Zbl 0308.93023)], applied in the presented stabilization procedure for computing the local feedback. An extensive illustrative example is included to clarify the method.