Abstract
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.
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