ℋ− index for continuous-time stochastic systems with Markov jump and multiplicative noise. (July 2019)

• Record Type: Journal Article
• Authors: Liu, Xikui; Zhang, Weihai; Li, Yan
• Is Part Of: Automatica. Volume 105(2019)
• Page Start: 167
• Page End: 178
• Publication Date: 2019-07
• Subjects: ℋ− index -- Fault detection -- Stochastic linear systems -- Markov jump; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2019.03.023
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: 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 s q u a r e systems is considered. Finally, the effectiveness of the obtained results is tested by two examples.