A Decentralized Stabilization Scheme for Large-scale Interconnected Systems

Abstract: This thesis considers the problem of decentralized control of large-scale systems by means of a decomposition and decentralization approach. Having decomposed the system into a number of interconnected subsystems a set of local decentralized controllers is constructed for individual subsystems. An important issue is to adapt methods with existing information structure constraints. Namely, sometimes exchange of information is not possible among various subsystems, or the transmission can be costly, lossy or delayed, which the latter, is usually unavoidable due to the prevailing technological trends of present-day, in using shared wireless networks. So the best way is that individual agents utilize their own locally available information for the purpose of control and estimation. Understandably, this constraint could also make the class of stabilizable systems smaller. Having described the basics of interconnected systems and decentralized control, a special class of stable systems is studied and an easy to follow algebraic solution for the stability of an interconnected system is put forward. Using the notion of diagonal dominance and some well known results from matrix theory, a decentralized stabilization scheme has been proposed for continuous and discrete time systems and the class of stabilizable systems has been identified using the linear programming technique. The design is reliable under structural perturbations by which subsystems are connected and disconnected again during the functioning of the system. Finally some nice properties of the mentioned class of stable systems are shown, especially the problem of robust stability for interval matrix family is considered and it is shown that this problem admits a simple solution for the studied family of systems.