Kim, Jung Hoon Hagiwara, Tomomichi 2024-01-20T05:01:53Z 2024-01-20T05:01:53Z 2022-01-25 2016-02 0020-7179 https://pubs.kist.re.kr/handle/201004/124423 This paper gives two methods for the L-1 analysis of sampled-data systems, by which we mean computing the L-infinity-induced norm of sampled-data systems. This is achieved by developing what we call the kernel approximation approach in the setting of sampled-data systems. We first consider the lifting treatment of sampled-data systems and give an operator theoretic representation of their input/output relation. We further apply the fast-lifting technique by which the sampling interval [0, h) is divided into M subintervals with an equal width, and provide methods for computing the L-infinity-induced norm. In contrast to a similar approach developed earlier called the input approximation approach, we use an idea of kernel approximation, in which the kernel function of an input operator and the hold function of an output operator are approximated by piecewise constant or piecewise linear functions. Furthermore, it is shown that the approximation errors in the piecewise constant approximation or piecewise linear approximation scheme converge to 0 at the rate of 1/M or 1/M-2, respectively. In comparison with the existing input approximation approach, in which the input function (rather than the kernel function) of the input operator is approximated by piecewise constant or piecewise linear functions, we show that the kernel approximation approach gives improved computation results. More precisely, even though the convergence rates in the kernel approximation approach remain qualitatively the same as those in the input approximation approach, the newly developed former approach could lead to quantitatively improved approximation errors than the latter approach particularly when the piecewise linear approximation scheme is taken. Finally, a numerical example is given to demonstrate the effectiveness of the kernel approximation approach with this scheme. English TAYLOR & FRANCIS LTD Further results on the L-1 analysis of sampled-data systems via kernel approximation approach Article 10.1080/00207179.2016.1144239 1 INTERNATIONAL JOURNAL OF CONTROL, v.89, no.8, pp.1684 - 1697 INTERNATIONAL JOURNAL OF CONTROL 89 8 1684 1697 N scie scopus 000380079600012 2-s2.0-84958057080 Automation & Control Systems Automation & Control Systems Article INFINITY-INDUCED NORM H(INFINITY) DESIGN FREQUENCY-RESPONSE GENERAL FRAMEWORK H(2) Sampled-data systems L-infinity-induced norm kernel approximation approach fast-lifting