Stabilizing bit-rate of disturbed event triggered control systems*

Event triggering is a sampling method where sampling occurs only if data 'novelty' exceeds a threshold. Prior work has demonstrated that event triggered systems have longer average sampling periods than periodic sampled systems with comparable system performance. Based on this fact, it is claimed that event triggered systems make more efficient use of communication resources than periodic sampled systems. If, however, we account for the number of bits in each sample and the maximum acceptable delay of this sample, it is possible that the bit-rates generated by event triggered systems are greater than that of periodic sampled systems. Our prior work in Li et al. [2012] has established, in noise-free cases, the condition under which the stabilizing bit-rates for quantized event-triggered systems converge asymptotically to a finite rate as the system approaches its equilibrium point. In some cases, this limiting bit-rate was shown to be 0. This paper extends that earlier work to quantized event-triggered systems with essentially bounded disturbances. Conditions on triggering event, quantization error and maximum delay are established to assure the input-to-state stability (ISS). The stabilizing bit-rate is, then, shown to be always bounded by a continuous, positive definite, increasing function with respect to the norm of the state. Since the system is ISS, the stabilizing bit-rate can be bounded from above by a function of time. This result provides a guide on how to assign communication resource to the control system. If we set external disturbance to be 0, the results in Li et al. [2012] are recovered.