Computing the L1-Induced Norm of Sampled-data Systems
Jung-Hoon Kim, Dohyeok Kwak, Jung Hoon Kim, Tomomichi Hagiwara · 2024
This paper is concerned with developing a method for computing the $L_{1}$-induced norm of sampled-data systems. We first derive an operator-based form of the $L_{1}$-induced norm in the lifted representation of sampled-data systems. The corresponding operators are further considered on the top of the fast-lifted treatment, in which the sampling interval [0, h) is divided into M subintervals with an equal width. This treatment allows us to develop a piecewise constant approximation of the input and output signals of sampled-data systems, by which an upper bound and a lower bound on the $L_{1}$-induced norm can be obtained. The gap between these bounds is shown to converge to 0 at the rate of 1/M with the fast-lifting parameter M.