TY - CHAP
T1 - Appendix
T2 - State-Variance Matrices
AU - van Schuppen, Jan H.
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
KW - Geometric structure
KW - Linear matrix inequality
UR - http://www.scopus.com/inward/record.url?scp=85112512060&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-66952-2_24
DO - 10.1007/978-3-030-66952-2_24
M3 - Chapter
AN - SCOPUS:85112512060
T3 - Communications and Control Engineering
SP - 897
EP - 916
BT - Control and System Theory of Discrete-Time Stochastic Systems
PB - Springer
ER -