Robust sliding mode design for uncertain stochastic systems based on \(H_\infty\) control method. (English) Zbl 1204.93133
Summary: In this paper, the design problem of Sliding Mode Control (SMC) is addressed for uncertain stochastic systems modeled by Itô differential equations. There exist parameter uncertainties in both the state and input matrices, as well as a unmatched external disturbance. The key feature of this work is the integration of SMC method with \(H_\infty\) technique such that the robust stochastic stability with a prescribed disturbance attenuation level \(\gamma \) can be achieved. A sufficient condition for the existence of the desired sliding mode controller is obtained via linear matrix inequalities. The reachability of the specified sliding surface is proven. Finally, a numerical simulation example is presented to illustrate the proposed method.
MSC:
| 93E20 | Optimal stochastic control |
| 93B36 | \(H^\infty\)-control |
| 93E15 | Stochastic stability in control theory |
| 93B12 | Variable structure systems |
Keywords:
stochastic systems; parameter uncertainties; external disturbance; sliding mode control; \(H_\infty\) controlReferences:
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