TY - GEN

T1 - Integral quadratic constraint theorem

T2 - 54th IEEE Conference on Decision and Control, CDC 2015

AU - Carrasco, Joaquin

AU - Seiler, Peter

PY - 2015/2/8

Y1 - 2015/2/8

N2 - This paper 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.

AB - This paper 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.

KW - Frequency-domain analysis

KW - Linear systems

KW - Nonlinear systems

KW - Stability analysis

KW - Standards

KW - Time-domain analysis

KW - Transfer functions

UR - http://www.scopus.com/inward/record.url?scp=84962006697&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84962006697&partnerID=8YFLogxK

U2 - 10.1109/CDC.2015.7403114

DO - 10.1109/CDC.2015.7403114

M3 - Conference contribution

AN - SCOPUS:84962006697

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 5701

EP - 5706

BT - 54rd IEEE Conference on Decision and Control,CDC 2015

PB - Institute of Electrical and Electronics Engineers Inc.

Y2 - 15 December 2015 through 18 December 2015

ER -