An L2-Consistent Data Transmission Sequence for Linear Systems

In this paper, we tackle the problem of selecting a sparse data transmission sequence for a networked control system while guaranteeing a certain ${\mathcal{L}_2}$-induced norm bound with respect to an exogenous disturbance input. As the main contribution of this work, for every periodic transmission sequence, we provide a transmission sequence counterpart, aperiodic in general, that results in fewer or at most the same number of transmissions while still guaranteeing an ${\mathcal{L}_2}$ control policy with the same ${\mathcal{L}_2}$-induced norm bound as that of the periodic transmission policy. In this sense, the proposed transmission sequence is called ${\mathcal{L}_2}$-consistent. Moreover, we show that as the horizon approaches infinity, the proposed ${\mathcal{L}_2}$consistent transmission sequence counterpart of every periodic transmission sequence approaches a periodic transmission sequence with an equal or larger time period.