Abstract
This paper addresses stability and observability of discrete-time mean-field stochastic systems with periodic coefficients and multiplicative noise. By constructing a monodromy operator associated to the periodic coefficients of the considered dynamics, spectral criterion and Lyapunov-type criterion are presented for asymptotic mean square stability and weak stability, respectively. Based on the Lyapunov criterion, a necessary and sufficient condition is supplied for regional stabilizability. Furthermore, Popov–Belevitch–Hautus (PBH) criterion is obtained for observability of mean-field stochastic periodic systems. By the proposed spectral criterion of stability/observability, the intrinsic relationships are clarified for stability/observability among deterministic periodic systems, stochastic periodic systems and mean-field stochastic periodic systems. Finally, as an application of PBH criterion, a Barbashin–Krasovskii stability theorem is established to indicate the connection between observability and stability of the considered systems.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
