Book contents
- Frontmatter
- Dedication
- Contents
- Preface and Acknowledgments
- Notation
- 1 Introduction
- 2 Preliminaries
- 3 Static Systems: Probabilistic Input Uncertainty
- 4 Static Systems: Probabilistic Structural Uncertainty
- 5 Discrete-Time Systems: Probabilistic Input Uncertainty
- 6 Continuous-Time Systems: Probabilistic Input Uncertainty
- 7 Static Systems: Set-Theoretic Input Uncertainty
- 8 Discrete-Time Systems: Set-Theoretic Input Uncertainty
- 9 Continuous-Time Systems: Set-Theoretic Input Uncertainty
- Appendix A Mathematical Background
- Appendix B Power Flow Modeling
- References
- Index
6 - Continuous-Time Systems: Probabilistic Input Uncertainty
Published online by Cambridge University Press: 17 January 2022
- Frontmatter
- Dedication
- Contents
- Preface and Acknowledgments
- Notation
- 1 Introduction
- 2 Preliminaries
- 3 Static Systems: Probabilistic Input Uncertainty
- 4 Static Systems: Probabilistic Structural Uncertainty
- 5 Discrete-Time Systems: Probabilistic Input Uncertainty
- 6 Continuous-Time Systems: Probabilistic Input Uncertainty
- 7 Static Systems: Set-Theoretic Input Uncertainty
- 8 Discrete-Time Systems: Set-Theoretic Input Uncertainty
- 9 Continuous-Time Systems: Set-Theoretic Input Uncertainty
- Appendix A Mathematical Background
- Appendix B Power Flow Modeling
- References
- Index
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.
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- Large-Scale System Analysis Under UncertaintyWith Electric Power Applications, pp. 166 - 201Publisher: Cambridge University PressPrint publication year: 2022