Stability of Nonlinear Systems with Two Time Scales Over a Single Communication Channel

This paper studies the stabilisation problem for a class of nonlinear systems with two time scales, where only a single communication channel is available to allocate both low and high-frequency transmissions from slow and fast subsystems, respectively. A clock mechanism is proposed to govern the transmissions, and the closed-loop system is modelled by a hybrid singularly perturbed system. Singular perturbation-based analysis is used to obtain individual maximum allowable transmission intervals for both slow and fast transmissions, and also to guarantee semi-global practical asymptotic stability with respect to the minimum allowable transmission interval of slow transmissions. We illustrate the results via a numerical example.