## Sliding mode control for time-varying delayed systems based on a reduced-order observer.(English)Zbl 1204.93029

Summary: A stabilisation problem for a class of nonlinear systems is considered, where both the nonlinear term and the nonlinear uncertainty are mismatched and subject to time-varying delay. Under the assumption that the delay is known, a reduced-order observer is designed using an appropriate transformation. A sliding surface is proposed in an augmented space formed by the system outputs and the estimated states. The sliding mode dynamics are derived using an equivalent control approach, and the Lyapunov-Razumikhin approach is exploited to analyse the stability of the sliding motion. Then, a sliding mode control law is developed such that the system can be driven to the sliding surface in finite time. A simulation example shows the effectiveness of the proposed approach.

### MSC:

 93B12 Variable structure systems 93C10 Nonlinear systems in control theory 93D20 Asymptotic stability in control theory 93D30 Lyapunov and storage functions
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### References:

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