Event-triggering stabilization of complex linear systems with disturbances over digital channels

As stops and pauses for separating parts of a sentence in language help to convey information, it is also possible to communicate information in communication systems not only by data payload, but also with its timing. We consider an event-triggering strategy that exploits timing information by transmitting in a state-dependent fashion to stabilize a continuous-time, complex, time-invariant, linear system over a digital communication channel with bounded delay and in the presence of bounded system disturbance. For small values of the delay, we show that by exploiting timing information, one can stabilize the system with any positive transmission rate. However, for delay values larger than a critical threshold, the timing information is not enough for stabilization and the sensor needs to increase the transmission rate. Compared to previous work, our results provide a novel encoding-decoding scheme for complex systems, which can be readily applied to diagonalizable multivariate system with complex eigenvalues. Our results are illustrated in numerical simulation of several scenarios.