Kim, Jung Hoon Hagiwara, Tomomichi 2024-01-20T00:03:57Z 2024-01-20T00:03:57Z 2021-09-05 2017-11 0020-7179 https://pubs.kist.re.kr/handle/201004/122097 This paper is concerned with linear time-invariant (LTI) sampled-data systems (by which we mean sampled-data systems with LTI generalised plants and LTI controllers) and studies their H-2 norms from the viewpoint of impulse responses and generalised H-2 norms from the viewpoint of the induced norms from L-2 to L infinity. A new definition of the H-2 norm of LTI sampled-data systems is first introduced through a sort of intermediate standpoint of those for the existing two definitions. We then establish unified treatment of the three definitions of the H-2 norm through a matrix function G(tau) defined on the sampling interval [0, h). This paper next considers the generalised H-2 norms, in which two types of the L infinity norm of the output are considered as the temporal suwpremum magnitude under the spatial 2-norm and infinity-norm of a vector-valued function. We further give unified treatment of the generalised H2 norms through another matrix function F(theta) which is also defined on [0, h). Through a close connection between G(t) and F(theta), some theoretical relationships between the H-2 and generalised H2 norms are provided. Furthermore, appropriate extensions associated with the treatment of G(t) and F(theta) to the closed interval [0, h] are discussed to facilitate numerical computations and comparisons of the H-2 and generalised H-2 norms. Through theoretical and numerical studies, it is shown that the two generalised H-2 norms coincide with neither of the three H-2 norms of LTI sampled-data systems even though all the five definitions coincide with each other when single-output continuous-time LTI systems are considered as a special class of LTI sampled-data systems. To summarise, this paper clarifies that the five control performance measures are mutually relatedwith each other but they are also intrinsically different from each other. English TAYLOR & FRANCIS LTD LINEAR PERIODIC-SYSTEMS L-INFINITY OPERATOR NORMS H2 CONVOLUTION Extensive theoretical/numerical comparative studies on H-2 and generalised H-2 norms in sampled-data systems Article 10.1080/00207179.2016.1257158 1 INTERNATIONAL JOURNAL OF CONTROL, v.90, no.11, pp.2538 - 2553 INTERNATIONAL JOURNAL OF CONTROL 90 11 2538 2553 scie scopus 000411339300018 2-s2.0-84996844881 Automation & Control Systems Automation & Control Systems Article LINEAR PERIODIC-SYSTEMS L-INFINITY OPERATOR NORMS H2 CONVOLUTION Sampled-data systems H-2 norm L-infinity/L-2-induced norm impulse response