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Robustness of Linear Periodically-Time-Varying Closed-Loop Systems.

Cantoni M. W. and Glover K.

Proceedings of the 37th IEEE CDC, December 1998

Abstract

This paper is concerned with the development of quantitative results that lead to a characterisation of the uncertainty types to which linear, periodically-time-varying (LPTV), closed-loop systems are insensitive. The results are expressed in terms of the gap metric, which is a measure of the distance between the graphs of two systems. Towards establishing the main results, a formula for the directed gap if derived for LPTV systems. This formula is essentially a generalisation of that given in \cite{georgiou}, for linear, time-invariant (LTI) systems. In fact, all of the results obtained in this paper are analogous to those known to hold for LTI systems cite{gs90,sefton} (although they do not follow directly from these). Importantly, the results presented in this paper apply to a class of sampled-data (SD) control-systems as a special case and are a step towards characterising the quality of SD approximations of LTI, continuous-time controllers.

BibTex Entry

@InProceedings{,: author = {Cantoni M. W. and Glover K.},; title = {Robustness of Linear Periodically-Time-Varying Closed-Loop Systems. },; address = {Tampa},; booktitle = {Proceedings of the 37th IEEE CDC},; month = {December},; year = {1998}
}



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