γ-Independent H∞-discretization of sampled-data systems by modified fast-sample/fast-hold approximation with fast lifting

This paper is concerned with H_infin-discretization for analysis and design of sampled-data control systems and provides a new method with an approximation approach called modified fast-sample/fast-hold approximation. By applying the fast-lifting technique, quasi-finite-rank approximation of an infinite-rank operator and then the loop-shifting technique, this new method can discretize the continuous-time generalized plant in a gamma-independent fashion even when the given sampled- data system has a nonzero direct feedthrough term from the disturbance input w to the controlled output z, unlike in the previous study. With this new method, we can obtain both the upper and lower bounds of the Z_infin-norm or the frequency response gain of any sampled-data systems regardless of the existence of nonzero D₁₁. Furthermore, the gap between the upper and lower bounds can be bounded with the approximation parameter N and is independent of the discrete-time controller. This feature is significant in applying the new method especially to control system design, and this study indeed has a very close relationship to the recent progress in the study of control system analysis/design via noncausal linear periodically time-varying scaling. We demonstrate the effectiveness of the new method through a numerical example.