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A control method is presented for the problem of decentralized stabilizationof large scale nonlinear systems by designing robust controllers, in the sense of L2-gaincontrol, for each subsystem. An uncertainty tolerance matrix is defined to characterize thedesired robustness leve1 of the overall system. It is then identified that, for a given uncer-tainty tolerance matrix, the design problem is related to the existence of a smooth Positivedefinite solution to a modified Ham ilton -Jacobi - Bellman (H-J-B ) equa tion. The solution,if exists, is exactly the payoff function in terms of the game theory. A decentralized statefeedback law is duly designed, which, under the weak assumption of the zero-state ob-servability on the system, renders the overall closed-loop system aspoptotically stable withan explicitly expressed stability region. Finally, relation between the payoff function andthe uncertainty tolerance matrix is provided, highlighting the “knowing less and payingmore” philosophy.
A control method is presented for the problem of decentralized stabilization of large scale nonlinear systems by designing robust controllers, in the sense of L2-gaincontrol, for each subsystem. It is an adaptive tolerance of large scale nonlinear systems by designing robust controllers then identified that, for a given uncer-tainty tolerance matrix, the design problem is related to the existence of a smooth Positivedefinite solution to a modified Ham ilton-Jacobi-Bellman (HJB) equa tion. The solution, if exists, is exactly the payoff function in terms of the game theory. A decentralized statefeedback law is duly designed, which, under the weak assumption of the zero-state ob-servability on the system, renders the overall closed-loop system aspoptotically stable withan explicitly expressed stability region. Finally, relation between the payoff function and the uncertainty tolerance matrix is provided, highlighting the “knowing less and payingmore” philosophy .