## Higher order sliding mode control based on integral sliding mode.(English)Zbl 1137.93338

Summary: A higher-order sliding mode control scheme for uncertain nonlinear systems is proposed in the present paper. It is shown that the problem is equivalent to the finite time stabilization of higher order input-output dynamics with bounded uncertainties $$(r \in \mathbb N)$$. The controller uses integral sliding mode concept and contains two parts. A part achieves finite time stabilization of the higher order input-output dynamics without uncertainties. The other part rejects bounded uncertainties throughout the entire response of the system. As a result, a higher order sliding mode is established. The advantages of the method are that its implementation is easy, the time convergence is chosen in advance and the robustness is ensured. An illustrative example of a car control shows the applicability of the method.

### MSC:

 93B51 Design techniques (robust design, computer-aided design, etc.) 93C10 Nonlinear systems in control theory 93C15 Control/observation systems governed by ordinary differential equations
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### References:

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