Asynchronous control of discrete-time stochastic bilinear systems with Markovian switchings. (English) Zbl 1482.93670
Summary: This paper is concerned with the problem of asynchronous control for a class of discrete-time Markov systems with multiplicative stochastic white noises. Based on a stability analysis scheme developed from mode-dependent Lyapunov function method, we first derive testable conditions in linear matrix inequality (LMI) setting to ensure the robust stability of the closed-loop system. We then recast the proposed stability conditions into equivalent forms that are later utilised to design a multi-mode asynchronous state-feedback controller (ASFC) that makes the closed-loop system stable. An extension to the case of deficient mode information (i.e. transition rates of the system and the controller are not fully accessible) is also presented. Finally, a model of networked control with DC devices is given to demonstrate the efficacy of the proposed design scheme.
MSC:
| 93E15 | Stochastic stability in control theory |
| 93C55 | Discrete-time control/observation systems |
| 93B52 | Feedback control |
| 60H40 | White noise theory |
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