Sliding-mode control for singularly perturbed systems

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Abstract
This paper addresses the design of sliding-mode controllers for singularly perturbed systems. The full-order system is separated into slow and fast subsystems and a sliding-mode controller is designed for each subsystem. A composite of these controls is then implemented on the full-order system. It is shown that if specific reaching conditions are satisfied for the reduced-order models and an additional condition is met, then the reaching conditions are also satisfied for the full-order model. Furthermore, sufficient conditions are derived which guarantee that the approximation error between the controlled reduced-order response and the controlled full-order model response is small. A numerical example is given which successfully demonstrates the techniques developed in this paper.