L∞-induced norm analysis of sampled-data systems via piecewise constant and linear approximations

This paper deals with the L 1 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 / M 2 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.