γ-Independent H∞-Discretization of Sampled-Data Systems by Modified Fast-Sample/Fast-Hold Approximation with Fast Lifting

This paper is concerned with H∞-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 γ-independent fashion even when the given sampleddata 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 H∞-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.