Controller design and stability analysis for singularly perturbed hybrid systems with multi-rate sampling

This paper investigates the stabilization problem of singularly perturbed hybrid systems with multi-rate sampling. Firstly, we establish a hybrid model to describe a class of singularly perturbed systems by designing a multi-rate sampling controller. Secondly, a sufficient condition is proposed to ensure that the considered systems are uniformly globally exponentially stable using the Lyapunov approach. Thirdly, we derive the bounds of the maximally allowable fast sampling interval, and analyze the relationship between the singular perturbation parameter and the fast sampling interval. Finally, a DC motor model is illustrated to demonstrate the effectiveness of the proposed approach.