Output Feedback Finite-Time Stabilization of Systems Subject to Hlder Disturbances via Continuous Fractional Sliding Modes
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abstract
The problem of designing a continuous control to guarantee finitetime tracking based on output feedback for a system subject to a Hlder disturbance has remained elusive. The main difficulty stems from the fact that such disturbance stands for a function that is continuous but not necessarily differentiable in any integerorder sense, yet it is fractionalorder differentiable. This problem imposes a formidable challenge of practical interest in engineering because (i) it is common that only partial access to the state is available and, then, output feedback is needed; (ii) such disturbances are present in more realistic applications, suggesting a fractionalorder controller; and (iii) continuous robust control is a must in several control applications. Consequently, these stringent requirements demand a sound mathematical framework for designing a solution to this control problem. To estimate the full state in finitetime, a highorder sliding modebased differentiator is considered. Then, a continuous fractional differintegral sliding mode is proposed to reject Hlder disturbances, as well as for uncertainties and unmodeled dynamics. Finally, a homogeneous closedloop system is enforced by means of a continuous nominal control, assuring finitetime convergence. Numerical simulations are presented to show the reliability of the proposed method.
