A Framework for Generalized Sampled-Data Control Systems and Its Application to Convergence Analysis

This paper presents a framework for sampled-data control systems with generalized samplers and holds. This framework is advantageous in the point that it covers a large class of generalized samplers and holds and also in the point that it treats samplers and holds in a symmetrical manner. Using this framework, converging and non-converging properties of sampled-data control are investigated. The best achievable performance of sampled-data control does not always converge to that of time-invariant continuous-time control as a sampling period approaches zero. This paper shows that the non-converging phenomenon occurs when a sampled-data system includes an anti-aliasing lter whose bandwidth is proportional to the Nyquist frequency or when it does not include an anti-aliasing lter. Moreover, this paper proves that one can avoid this non-converging phenomenon for almost all G using a special sampler-hold pair.