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Stabilization of Cascaded Two-Port Networked Systems with Simultaneous Nonlinear Uncertainties

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Document pages: 16 pages

Abstract: We introduce a versatile framework to model and study networked controlsystems (NCSs). An NCS is described as a feedback interconnection of a plantand a controller communicating through a bidirectional channel modelled bycascaded nonlinear two-port networks. This model is sufficiently rich tocapture various properties of a real-world communication channel, such asdistortion, interference, and nonlinearity. Uncertainties in the plant,controller and communication channels can be handled simultaneously in theframework. We provide a necessary and sufficient condition for the robustfinite-gain stability of an NCS when the model uncertainties in the plant andcontroller are measured by the gap metric and those in the nonlinearcommunication channels are measured by operator norms of the uncertainelements. This condition is given by an inequality involving "arcsine " of theuncertainty bounds and is derived from novel geometric insights underlying therobustness of a standard closed-loop system in the presence of conelikenonlinear perturbations on the system graphs.

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