Kernel Approximation Approach to the L1 Optimal Sampled-Data Controller Synthesis Problem

Abstract

This paper is concerned with a new framework called the kernel approximation approach to the L1 optimal controller synthesis problem of sampled-data systems. On the basis of the lifted representation of sampled-data systems, which contains an input operator and an output operator, this paper introduces a method for approximating the kernel function of the input operator and the hold function of the output operator by piecewise constant functions. Through such a method, the L1 optimal sampled-data controller synthesis problem could be (almost) equivalently converted into the discrete-time l1 optimal controller synthesis problem. This paper further establishes an important inequality that forms the theoretical validity of the kernel approximation approach for tackling the L1 optimal sampled-data controller synthesis problem.