Generalized framework for computing the [formula omitted]-induced norm of sampled-data systems

Abstract

This paper develops a generalized framework for computing the L∞-induced norm of sampled-data systems, by which we mean those consisting of a continuous-time linear time-invariant (LTI) plant and a discrete-time LTI controller, and such systems have a linear periodically time-varying (LPTV) nature. In the authors’ preceding studies, the input/output relation of sampled-data systems was described in an operator-theoretic fashion, and the kernel and input functions of an input operator and the hold function of an output operator were approximated by piecewise lth order polynomials with l=0,1. This leads to an approximate computation of this norm, where the computation errors were shown to converge to 0 in the order of 1/Ml+1 as the approximation parameter M becomes larger. Along this line, we aim at improving the computation performance compared to the preceding studies by considering the freedom in the point around which the corresponding functions are expanded to a Taylor series. This leads to a generalization of the piecewise lth order approximations, and we show that taking the central point for the Taylor expansion leads to quantitatively improved accuracy than that of our preceding results that take an edge point.Finally, the effectiveness of the developed method is verified through a numerical example.