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access icon free Spectral perspective on stability and stabilisation of continuous-time mean-field stochastic systems

  • Author(s): Limin Ma 1 ; Weihai Zhang 2 ; Jianwei Xia 3
    • View affiliations
  • Source: Volume 13, Issue 8, 21 May 2019, p. 1137 – 1146
    DOI:  10.1049/iet-cta.2019.0072 , Print ISSN 1751-8644, Online ISSN 1751-8652
© The Institution of Engineering and Technology
Received 16/01/2019, Accepted 20/03/2019, Published 25/03/2019

This mainly studies the mean square stabilisability, interval stability and stabilisation of mean-field stochastic control systems. A necessary and sufficient condition for stabilisation of continuous-time mean-field stochastic systems is presented via operator spectrum technique. The unremovable spectrum is generalised to mean-field stochastic differential equations (MF-SDEs), and a necessary and sufficient condition for unremovable spectrum is obtained. Three operators defined in different domains are given to characterise the stabilisability of MF-SDEs. As applications, an example is given to illustrate their relationships. Interval stability and stabilisation are generalised to MF-SDEs, and a necessary condition for interval stability is given to show the relationship among interval stability, the decay rate of the system state response and the Lyapunov exponent. A sufficient condition for interval stabilisation is proposed via linear matrix inequality approach.

Inspec keywords: stability; stochastic processes; stochastic systems; differential equations; Lyapunov methods; linear matrix inequalities

Other keywords: mean-field stochastic differential equations; interval stability; interval stabilisation; unremovable spectrum; operator spectrum technique; mean square stabilisability; mean-field stochastic control systems; MF-SDEs; sufficient condition; continuous-time mean-field stochastic systems; necessary condition

Subjects: Optimal control; Time-varying control systems; Stability in control theory; Algebra

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