Modified fast-sample/fast-hold approximation for sampled-data system analysis

This paper deals with the H
_∞
norm and frequency response gain analysis of sampled-data systems and provides a new approach, which we call modified fast-sample/fast-hold approximation. The new approximation approach discretizes the continuous-time generalized plant in a “γ-independent fashion” and leads to a discrete-time generalized plant with a similar structure to what is obtained by the conventional fast-sample/fast-hold approximation approach. Unlike the conventional approach, however, the modified fast-sample/fast-hold approximation approach can give both the upper and lower bounds of the H
_∞
-norm and/or the frequency response gain for sampled-data systems. Furthermore, the gap between the upper and lower bounds can be bounded from above directly from the fast-sample/fast-hold parameter N and is independent of the controller. These features are quite useful when it is applied to control system design, and this study indeed has very close relation with the control system design via noncausal periodically time-varying scaling, a novel notion introduced recently.