Appendix

van Schuppen, J.H.

Appendix

State-Variance Matrices

Book chapter (2021)

Authors

J.H. van Schuppen Mathematical Physics -

Research Group

Mathematical Physics () (TU Delft)

Linear matrix inequality Geometric structure

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Published Date

2021

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Mathematical Physics

Abstract

Concepts and results of the geometric structure of the set of state-variance matrices of a time-invariant Gaussian system are provided in this chapter. With respect to a condition, the set is convex with a minimal and a maximal element. In case the noise variance matrix satisfies a nonsingularity condition, the matrix inequality is equivalent to an inequality of Riccati type. The singular boundary matrices of the set of state variances play a particular role. Finally, the classification of all elements of the set of state variances can be described in terms of an increment above the minimal element or below the maximal element, which increments satisfy a Lyapunov equation.