L&lt;inf&gt;1&lt;/inf&gt; analysis of LTI systems via piecewise higher-order approximation

Choi, Yong Woo; Hagiwara, Tomomichi

doi:10.1109/cca.2015.7320809

Cited by 2 publications

(1 citation statement)

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“…Very importantly, the improvement over our earlier studies [19], [20] is not limited simply to the use of such higher order approximation schemes (and establishing theoretical bases for these schemes) but includes generalized arguments relevant to how the Taylor expansion of relevant functions is used; even though the earlier studies only considered the Taylor expansion at the beginning of each subintervals resulting from the application of fast-lifting, this paper considers taking advantage of the freedom in the time instant around which relevant functions are expanded to Taylor series. In this respect, this paper corresponds to a significantly extended version of an earlier conference paper by the authors [22], which discussed the development of the piecewise quadratic and cubic approximation schemes for the first time (without associated proofs and numerical examples). Under such generalized treatment, it is once again shown that the kernel approximation approach is quantitatively superior to the input approximation approach in terms of the gap between the upper and lower bounds, even though the convergence rate itself (as mentioned above) is shared by the two approaches under the same approximation order.…”

Section: A Related Studies On the L∞-induced Norm Analysismentioning

confidence: 99%

Computing the L∞-Induced Norm of LTI Systems: Generalization of Piecewise Quadratic and Cubic Approximations

Choi

Hagiwara

2020

IEEE Access

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This paper is concerned with performance analysis for bounded persistent disturbances of continuous-time linear time-invariant (LTI) systems. Such an analysis can be done by computing the L ∞induced norm of continuous-time LTI systems since it corresponds to the worst maximum magnitude of the output for the worst persistent external input with a unit magnitude. In our preceding study, piecewise constant and linear approximation schemes for analyzing this norm have been developed through two alternative approximation approaches, one for the input and the other for the relevant kernel function, via the fast-lifting technique. The approximation errors in these approximation schemes have been shown to converge to 0 at the rates of 1/N and 1/N 2 , respectively, as the fast-lifting parameter N is increased. Along this line, this paper aims at developing generalized techniques that offer improved accuracy named the piecewise quadratic and cubic approximation schemes. The generalization and the associated accuracy improvement discussed in this paper are not limited to the increased orders of approximation but are extended further to taking advantage of the freedom in the point around which relevant functions are expanded to Taylor series. The approximation errors in the piecewise quadratic and cubic approximation schemes are shown to converge to 0 at the rates of 1/N 3 and 1/N 4 , respectively, regardless of the point at which the Taylor expansion is applied. Finally, effectiveness of the developed computation methods is confirmed through a numerical example. INDEX TERMS Approximate computing, approximation methods, linear systems, performance analysis, robustness.

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Section: A Related Studies On the L∞-induced Norm Analysismentioning

confidence: 99%