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Decentralized control for large–scale systems with time–varying delay and unmatched uncertainties. (English) Zbl 1242.93007
Summary: Many real-world systems contain uncertainties and with time-varying delays, also, they have become larger and more complicated. Hence, a new decentralized variable structure control law is proposed for a class of uncertain large-scale system with time varying delay in the interconnection and time varying unmatched uncertainties in the state matrix. The proposed decentralized control law for the large-scale time-varying delay system is realized independently through the delayed terms and it can drive the trajectories of the investigated systems onto the sliding mode. Further, the proposed control law can be successfully applied to stabilize a class of uncertain large-scale time-varying delay system with matched and unmatched uncertainties. The so-called sliding coefficient matching condition can be extended for the decentralized variable structure control of the uncertain large-scale time-varying delay systems. Furthermore, in the sliding mode, the investigated system with matched and unmatched uncertainties still bears the insensitivity to the uncertainties and disturbances, which is the same as the systems with just matched uncertainties do. Finally, an illustrative example is given to verify the validity of the proposed decentralized variable structure control law. It has been shown that the proposed decentralized control law is effective for all subsystems of the investigated system. However, the traditional decentralized variable structure control law is not applicable to the investigated system with unmatched uncertainties. It is worth noting that the traditional large-scale system is only a special case in this work.
93A15 Large-scale systems
93B12 Variable structure systems
93C10 Nonlinear systems in control theory
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93A14 Decentralized systems
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