Worst-case performance and stability of multirate sampled-data systems with nonsynchronous decentralized controllers

This paper focuses on multi-rate sampled-data control of large-scale systems with nonsynchronous decentralized controllers whose sampler-and-hold elements in different stations update their state independently of each other. Phases of discrete-time events in decentralized control stations are different because of digital control with multiple processors although each controller in a station is a synchronous single-rate sampled-data controller. The paper analyzes the effect of the nonsynchronous phase distribution on L^P worst-case performance and stability. A new representations for analyzing and assessing performance degradation caused by the nonsynchronism are presented. The method of analysis is further modified to propose an approach to design of L^P-gain suboptimal nonsynchronous multi-rate controllers. Some results on stability and performance robustness for the nonsynchronous closed-loop system are developed