## Observer-based sliding mode control for nonlinear state-delayed systems.(English)Zbl 1059.93025

The authors consider a state-delayed control system with unmeasurable states, mismatched parameter uncertainties and an unknown nonlinear function. First, under suitable assumptions, it is proved that the sliding mode dynamics, restricted to a suitable sliding surface, is asymptotically stable. Next, a sliding mode observer is constructed to estimate the state variables. By means of feasibility of some linear matrix inequalities, a sufficient condition is proved to ensure asymptotic stability of the closed-loop system composed of the state observer and the estimation error system. It is also proved that the proposed control scheme guarantees reachability of the sliding surfaces in both the state estimate space and the estimation error space. A simulation example is also presented.

### MSC:

 93B12 Variable structure systems 93C23 Control/observation systems governed by functional-differential equations 15A39 Linear inequalities of matrices 93D15 Stabilization of systems by feedback
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### References:

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