Dynamic Output-Feedback Control for Multirate Positive Systems Under Round-Robin Protocol

This article is devoted to the problem of dynamic output-feedback control for a class of discrete-time multirate systems under the scheduling of the Round-Robin (R-R) communication protocol. In order to reflect the practical engineering characteristic, the sampling interval of the sensors and the updating interval of the system states may differ. Firstly, we use a lifting approach to obtain an equivalent single-rate system by increasing the state update period, thus making the system analysis easier. Secondly, a dynamic output-feedback controller under the R-R scheduling scheme is constructed to mitigate undesired data congestions. At every sample time, only a single sensor can gain access and send its measured value under the R-R scheduling. Then, we give sufficient conditions for the controlled system to be exponentially stable, positive, and has an \(l_1\) -gain bound \(\gamma \) . Furthermore, the predicted controller gain matrices are obtained with precise formulas.