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University of Cambridge > Talks.cam > CUED Control Group Seminars > Integral Quadratic Constraint Theorem: A topological separation approach

## Integral Quadratic Constraint Theorem: A topological separation approachAdd to your list(s) Download to your calendar using vCal - Joaquin Carrasco Gomez, University of Manchester
- Thursday 14 January 2016, 14:00-15:00
- Cambridge University Engineering Department, LR5.
If you have a question about this talk, please contact Tim Hughes. This seminar concerns the input/output stability of two systems in closed-loop where stability is ensured by using open-loop properties of each subsystem. The literature is divided into consideration of time-domain and frequency-domain conditions. A complete time-domain approach is given by dissipative and topological separation theory, where both conditions are given in the time-domain. On the other hand, the frequency-domain integral quadratic constraints (IQCs) framework uses only frequency-domain conditions. Between both extremes, the classical multiplier approach and the time-domain IQC framework can be seen as hybrid versions where one condition is tested in the time-domain and other condition is tested in the frequency-domain. The time-domain is more natural for nonlinear systems, and subsystems may be unbounded in time-domain analysis. However, the frequency-domain has two advantages: firstly if one block is linear, then frequency-domain analysis leads to elegant graphical and/or LMI conditions; secondly noncausal multipliers can be used. Recently the connection between frequency domain IQCs and dissipativity has been studied. Here we use graph separation results to provide a unifying framework. In particular we show how a recent factorization result establishes a straightforward link, completing an analysis suggested previously. This factorization leads to a simple and insightful dissipative condition to analyse stability of the feedback interconnection. This talk is part of the CUED Control Group Seminars series. ## This talk is included in these lists:- All Talks (aka the CURE list)
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