Time-convexity and time-gain-scheduling in finite-horizon robust H∞-control

S. Boyarski, U. Shaked

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


A simple efficient method for addressing finite-horizon control problems is suggested for a class of linear time-varying systems by solving 'standard' (algebraic) linear matrix inequalities (LMIs). Considering the Lyapunov function x T P(t)x, a class of time-varying solutions for P(t) is derived without using differential inequalities. The core idea is to seek a P(t) which is linear in time, and to exploit convexity in normalized time over the scenario duration (or over each time sub-interval, in the piecewise version) in order to reduce the differential LMIs, which result from the bounded real lemma, to algebraic LMIs at the scenario (or sub-intervals) end-points. The resulting state-feedback gain is explicitly time-scheduled. The method can simultaneously cover polytopic parametric uncertainties, and can be applied together with the 'best-mean' approach.
Original languageUndefined/Unknown
Title of host publicationProceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference
Number of pages6
StatePublished - Dec 2009
EventProceedings of the 48h IEEE Conference on Decision and Control - Shanghai, China, China
Duration: 15 Dec 200918 Dec 2009

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216


ConferenceProceedings of the 48h IEEE Conference on Decision and Control
CityShanghai, China
Internet address

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