Nyström, AntonRenganathan, VenkatramanCantoni, Michael2025-03-122025-03-122024-12-16Nyström A, Renganathan V, Cantoni M. (2024) Stereographic projection of probabilistic frequency-domain uncertainty. In: Proceedings of the 2024 IEEE 63rd Conference on Decision and Control (CDC). 16 Dec 2024 - 19 Dec 2024, Milan, Italy, pp. 4411-4417https://doi.org/10.1109/cdc56724.2024.10886455https://dspace.lib.cranfield.ac.uk/handle/1826/23594This paper investigates the stereographic projection of points along the Nyquist plots of single input single output (SISO) linear time invariant (LTI) systems subject to probabilistic uncertainty. At each frequency, there corresponds a complex-valued random variable with given probability distribution in the complex plane. The chordal distance between the stereographic projections of this complex value and the corresponding value for a nominal model, as per the well-known ν-Gap metric of Vinnicombe, is also a random quantity. The main result provides the cumulative density function (CDF) of the chordal distance at a given frequency. Such a stochastic distance framework opens up a fresh and a fertile research direction on probabilistic robust control theory.pp. 4411-4417enAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/4901 Applied Mathematics49 Mathematical Sciences4007 Control Engineering, Mechatronics and Robotics40 EngineeringRobust controlMeasurementLinear systemsUncertaintySISOFrequency-domain analysisStochastic processesProbabilistic logicProbability distributionRandom variablesConference paper979-8-3503-1633-92576-2370566131