A class of transformation matrices and its applications. (English) Zbl 1406.93082

Summary: This paper studies a class of transformation matrices and its applications. Firstly, we introduce a class of transformation matrices between two different vector operators and give some important properties of it. Secondly, we consider its two applications. The first one is to improve Qian Jiling’s formula. And the second one is to deal with the observability of discrete-time stochastic linear systems with Markovian jump and multiplicative noises. A new necessary and sufficient condition for the weak observability will be given in the second application.


93B17 Transformations
93C55 Discrete-time control/observation systems
93B07 Observability
93C05 Linear systems in control theory
93E03 Stochastic systems in control theory (general)
60J75 Jump processes (MSC2010)
Full Text: DOI


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