K. Okano, M. Wakaiki, G. Yang and J. P. Hespanha, Stabilization of Networked Control Systems Under Clock Offsets and Quantization, IEEE Transactions on Automatic Control, vol. 63, no. 6, pp. 1708-1723 DOI: 10.1109/TAC.2017.2753938.
This paper studies the impact of clock mismatches and quantization on networked control systems. We consider a scenario where the plant’s state is measured by a sensor that communicates with the controller through a network. Variable communication delays and clock jitter do not permit a perfect synchronization between the clocks of the sensor and controller. We investigate limitations on the clock offset tolerable for stabilization of the feedback system. For a process with a scalar-valued state, we show that there exists a tight bound on the offset above which the closed-loop system cannot be stabilized with any causal controllers. For higher dimensional plants, if the plant has two distinct poles, then the effect of clock mismatches can be canceled with a finite number of measurements, and hence there is no fundamental limitation. We also consider the case where the measurements are subject to quantization in addition to clock mismatches. For first-order plants, we present necessary conditions and sufficient conditions for stabilizability, which show that a larger clock offset requires a finer quantization.