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6 - Continuous-Time Systems: Probabilistic Input Uncertainty

Published online by Cambridge University Press:  17 January 2022

Alejandro D. Domínguez-García
Affiliation:
University of Illinois, Urbana-Champaign
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Summary

This chapter studies continuous-time dynamical systems described by a continuous-time state-space model whose input is subject to probabilistic uncertainty. The first part of the chapter is devoted to the analysis of linear systems and provides techniques for computing the first and second moments of the state vector when the evolution of the input vector is governed by a "white noise" process with known mean and covariance functions. Then, by additionally imposing this white noise process to be Gaussian, we provide a partial differential equation whose solution yields the pdf of the state vector. The second part of the chapter extends these techniques to the analysis of nonlinear systems, with a special focus on the case when the white noise governing the evolution of the input vector is Gaussian. The third part of the chapter illustrates the application of the techniques developed to the analysis of inertia-less AC microgrids when the measurements utilized by the frequency control system are corrupted by additive disturbances.

Type
Chapter
Information
Large-Scale System Analysis Under Uncertainty
With Electric Power Applications
, pp. 166 - 201
Publisher: Cambridge University Press
Print publication year: 2022

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