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Computing the L-2 gain for linear periodic continuous-time systems
KTH, School of Electrical Engineering (EES), Automatic Control.ORCID iD: 0000-0003-1835-2963
2009 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 45, no 3, 783-789 p.Article in journal (Refereed) Published
Abstract [en]

A method to compute the L-2 gain is developed for the class of linear periodic continuous-time systems that admit a finite-dimensional state-space realisation. A bisection search for the smallest upper bound on the gain is employed, where at each step an equivalent discrete-time problem is considered via the well known technique of time-domain lifting. The equivalent problem involves testing a bound on the gain of a linear shift-invariant discrete-time system, with the same state dimension as the periodic continuous-time system. It is shown that a state-space realisation of the discrete-time system can be constructed from point solutions to a linear differential equation and two differential Riccati equations, all subject to only single-point boundary conditions. These are well behaved over the corresponding one period intervals of integration, and as such, the required point solutions can be computed via standard methods for ordinary differential equations. A numerical example is presented and comparisons made with alternative techniques.

Place, publisher, year, edition, pages
2009. Vol. 45, no 3, 783-789 p.
Keyword [en]
Norms, Linear systems, Time-varying systems, Computational methods, sampled-data control, h-infinity norm, numerical-integration, theoretical aspects, frequency-response, riccati equation, issues
National Category
Control Engineering
URN: urn:nbn:se:kth:diva-18292DOI: 10.1016/j.automatica.2008.10.018ISI: 000264576400024ScopusID: 2-s2.0-60449101678OAI: diva2:336338

QC 20111110

Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2016-06-01Bibliographically approved

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Sandberg, Henrik
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