Generalized Fast-Hold Approximation Approach to Sampled-Data L1 Synthesis

Abstract

This paper introduces a new framework for the synthesis of a sampled-data L1 controller, by which the L∞-induced norm of sampled-data systems is minimized. More precisely, we develop an idea of generalized version of the conventional fast-hold approximation operator by taking the freedom in the point at which the hold approximation of functions on subintervals of the sampling interval [0, h) is concerned with. Taking this generalized operator for the output function together with the conventional fast-averaging operator for the input function of sampled-data systems leads to approximate discrete-time systems, by which the sampled-data L1 synthesis problem is converted to the discrete-time l1 synthesis problem. An important inequality is further established to ensure the convergence rate of 1/M with respect to the associated performance deterioration, regardless of where the corresponding approximation parameter M is taken. This inequality also clarifies that the performance deterioration could be minimized when the central points in the M subintervals are taken.