Stabilization of cascaded two-port networked systems with simultaneous nonlinear uncertainties

We investigate the robust stability of a networked control system (NCS) subject to simultaneous nonlinear uncertainties. An NCS is described as a feedback interconnection of a plant and a controller communicating through a bidirectional channel modeled by cascaded nonlinear two-port networks. This model is sufficiently rich to capture various properties of a real-world communication channel, such as distortion, interference, and nonlinearity. We provide a necessary and sufficient condition for the robust finite-gain stability of such an NCS when the model uncertainties in the plant and controller are measured by the gap metric and those in the nonlinear channels are measured by operator norms of the uncertain elements. This condition is given by an inequality involving “arcsine” of the uncertainty bounds and is derived from novel geometric insights underlying the robustness of a standard closed-loop system in the presence of conelike nonlinear perturbations on the system graphs.