Controllability of Networked Sampled-Data Systems With Time Delays

This article investigates the controllability of networked sampled-data systems with various time delays on both control and transmission channels. Necessary and sufficient controllability conditions are first derived for systems with a single delay and then extended to systems with multiple delays. It is found that delays in control signals have no effects on the overall controllability. For a networked system whose topology matrix has only zero eigenvalues, delays of neither control nor transmission signals will affect the overall controllability. It is proved that an uncontrollable mode 1 of such a networked sampled-data system cannot be altered by arbitrary delays. Finally, the networked sampled-data system with first-order holders is discussed, which is modeled as a variant of time-delayed system, and some easy-to-verify algebraic conditions on the controllability are given based on matrix rank checking.