ℋ− index for continuous-time stochastic systems with Markov jump and multiplicative noise

This paper investigates the problem of ℋ− index for stochastic linear continuous-time systems involving Markov jump and multiplicative noise. A set of generalized differential Riccati equations (GDREs) are presented and it is shown that the solvability of GDREs is necessary and sufficient for the fe...

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Bibliographic Details
Published inAutomatica (Oxford) Vol. 105; pp. 167 - 178
Main Authors Liu, Xikui, Zhang, Weihai, Li, Yan
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.07.2019
Subjects
[formula omitted] index
Fault detection
Markov jump
Stochastic linear systems
ℋ− index
Markov jump
Fault detection
Stochastic linear systems
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Summary:This paper investigates the problem of ℋ− index for stochastic linear continuous-time systems involving Markov jump and multiplicative noise. A set of generalized differential Riccati equations (GDREs) are presented and it is shown that the solvability of GDREs is necessary and sufficient for the feasibility of an ℋ−index larger than γ>0. Our results extend the corresponding deterministic cases to stochastic systems. Furthermore, the infinite horizon ℋ− index problem for square systems is considered. Finally, the effectiveness of the obtained results is tested by two examples.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2019.03.023