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Correspondence- Decentralized Stabilization of Large-Scale Dynamical Systems M. DARWISH, H. M. SOLIMAN, AND J. FANTIN Abstract-The problem of stabilizing large-scale linear time invariant systems is considered. An approach is developed for stabilization using sets of decentralized controllers, and sufficient conditions are established in a form of algebraic criteria which can guarantee the stability under certain structural perturbations. I. INTRODUCTION In classical control theory the systems under study are assumed to have only one control agent (called a controller) who deter- mines the control actions based on the available information of the system. Systems of this type are called centralized systems, Li [1]. With the development of modern technology the size and com- plexity of the systems are increasing every day making the cen- tralized control practically undesirable due to the cost of transmission of information to the central controller, in addition there might exist important delays and/or institutional constraints in carrying out central control actions [2], [3]. Hence large-scale systems are an essential feature of our present society. An example of a large-scale system is a system of electric power networks belonging to several electric power generating com- panies connected together by tie lines where operators and dispat- chers of each company have direct control of power generation and regulation of frequency and voltage in their own regions, but have no direct controls in regions belonging to different power companies. Hence dynamic behavior in these networks is influenced by several control agents acting partially independent of each other [4], [5]. Another example of a large-scale system is computer communi- cation networks, whether land based or satellite, having a message routing between terminals where each terminal does not have Manuscript received March 7, 1978; revised November 8, 1978 and July 3, 1979. M. Darwish and H. M. Soliman are with Laboratoire d'Automatique et d'Analyse' des Systemes du C.N.R.S. 7, Avenue du Colonel Roche, 31400 Toulouse, France, on leave from the Department of Electrical Engineering, Cairo University, Cairo, Egypt. J. Fantin is with Laboratoire d'Automatique et d'Analyse des Systemes du C.N.R.S. 7, Avenue du Colonel Roche, 31400 Toulouse, France. access to information available to the other terminals. Here we have a team decision problem of maximizing the overall system performance [2], [6], [7]. In spite of the natural existence of large-scale systems no common precise definition for largeness has been proposed. The large-scale system we will adopt here is a system consisting of a number of interdependent subsystems which serve particular functions, share resources, and are governed by a set of inter- related goals and constraints [8], [9]. Much of the early work done in the area of large-scale systems is centered around the development of multilevel decomposition and coordination methods [9], [10], [11]. Although these techniques are conceptually simple, they require iterative solution procedures which may lead to convergent difficulties [12], [13]. Other multilevel schemes are based on characterization of interac- tions as perturbation signals acting in contradiction to the auton- omy of the individual subsystems, then compensating signals that account for the interconnection effects are used in conjunction with locally decentralized controllers [14], [15], [16]. However, the multilevel methods can give the solution in opti- mal manner it requires high communication cost between the subsystems and the coordinator, besides, the stability of the system may be lost if a fault occurred in the communication links. Due to these difficulties decentralized control becomes vital in the case where one can dispense some of the optimality. By decentralized systems we mean systems having several local control stations where at each station the controller observes only local system outputs and controls only local inputs. All the con- trollers are involved, however, in controlling the overall large system. In decentralized control the problem of stability of the overall system becomes very important, this problem has received the attention of many authors in the last few years [1], [3], [4], [16], [17]. Attention is given to the construction of appropriate control- lability subspaces and canonical form in the subsystems descrip- tions and to the derivation of necessary and sufficient conditions for the existence of local controllers to stabilize a given system using either static or dynamic compensators. In this correspondence an approach for the decentralized stabi- lization of a large-scale linear dynamical system is developed. Sufficient conditions for decentralized stabilization in a form of algebraic criteria are established which can guarantee the stability under certain structural perturbations. Finally the theory developed in this correspondence is illustrated by an example. 0018-9472/79/1100-0717$00.75 © 1979 IEEE 717