Lp analysis of nonsynchronous multirate sampled-data systems: continuity property and robustness

Focuses on multirate sample-data control systems with nonsynchronous decentralized controllers whose sampler-and-hold elements in different stations update their state independently of each other. The effect of nonsynchronous phase distribution on L^p worst-case performance is analyzed. It is shown that the performance measure is a continuous function of the phase shift provided that anti-aliasing filters are located appropriately. Slight perturbation of the phase only results in a slight degradation or improvement of the closed-loop performance. Furthermore, the analysis of the continuity property enables us to estimate how robust the performance is against the phase perturbation