Abstract
This paper deals with the L1 analysis of linear sampled-data systems, by which we mean the computation of the L∞-induced norm of linear sampled-data systems. Two computation methods based on piecewise constant and piecewise linear approximations are provided through fast-lifting, by which the sampling interval [0,h) is divided into M subintervals with an equal width. Even though the central part of the method with the former approximation essentially coincides with a conventional method via fast-sample/fast-hold (FSFH) approximation after all, we show that both methods successfully lead to the upper and lower bounds of the L∞-induced norm, whose gap converges to 0 at the rate of 1/M in the former approximation and 1/M2 in the latter extended approximation. Such achievements are in sharp contrast with an existing result on the former (i.e., FSFH) approximation, which only shows the convergence rate of the error in the resulting estimate of the L∞-induced norm, without providing any readily computable upper and lower bounds. A numerical example is given to illustrate the effectiveness of these methods.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.