Stabilisation of two-time scale systems with a finite feedback data rate [Brief Paper]

This study investigates a stabilisation problem of two-time scale systems with a finite feedback data rate. The uniform estimate of the state growth rate over each sampling interval is first provided, which is shown to be independent of the small parameter. Then, based on the given uniform estimate and the decoupled form of the two-time scale systems, the requirement, which is independent of the small parameter, on the necessary data rate for the channel is derived through the design of a quantiser. Based on this requirement, the authors obtain the detecting systems, which are two-time scale hybrid systems with impulsive. Then, under the assumption of strong controllability of the original two-time scale systems, it is shown that there exists a bound of the small parameter such that the original two-time scale systems are stabilised by a quantised state via a finite feedback data rate channel for a small parameter within the bound. Finally, a simulation example illustrates the result.