Stabilization of stochastic delay systems via a disordered controller. (English) Zbl 1426.93359
Summary: In this paper, the stabilization for stochastic delay systems is achieved by a disordered controller. Different from the traditionally stabilizing controllers, the controller designed here experiences a disorder between control gains and system states. By exploiting the robust method, the above disorder is described as a controller having special uncertainties. Moreover, the probability distribution of such uncertainties is embodied by a Bernoulli variable. A sufficient condition for the existence of such a disordered controller is given with LMIs, where the probability is considered in its design procedure. Based on this description, a more general but complicated case where the corresponding probability is not exact but has a uncertainty is further studied, whose LMI conditions are presented too. Finally, a numerical example is exploited to demonstrate the effectiveness and superiority of the proposed methods.
MSC:
| 93E15 | Stochastic stability in control theory |
| 34K20 | Stability theory of functional-differential equations |
| 34K50 | Stochastic functional-differential equations |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 93D15 | Stabilization of systems by feedback |
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