SICE Journal of Control, Measurement, and System Integration
Online ISSN : 1884-9970
Print ISSN : 1882-4889
ISSN-L : 1882-4889
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LMI-Based Lower Bound Analysis of the Best Achievable H Performance for SISO Systems
Yoshio EBIHARAKeisuke MATSUOTomomichi HAGIWARA
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2016 Volume 9 Issue 4 Pages 165-172

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Abstract

In this paper, we study H performance limitation analysis for continuous-time SISO systems using LMIs. By starting from an LMI that characterizes a necessary and sufficient condition for the existence of desired controllers achieving a prescribed H performance level, we represent lower bounds of the best H performance achievable by any LTI controller in terms of the unstable zeros and the unstable poles of a given plant. The transfer functions to be investigated include the sensitivity function (1+PK)-1, the complementary sensitivity function (1+PK)-1PK, and (1+PK)-1P, the first and the second of which are well investigated in the literature. As a main result, we derive lower bounds of the best achievable H performance with respect to (1+PK)-1P assuming that the plant has unstable zeros. More precisely, we characterize a lower bound in closed-form by means of the first non-zero coefficient of the Taylor expansion of the plant P(s) around its unstable zero.

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© 2016 The Society of Instrument and Control Engineers
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