New algorithmic approach based on integral quadratic constraints for stability analysis of high order models

Abstract

To analyze a non linear closed loop which represents a high order aeroelastic model of a large civil aircraft interconnected with non-linearities, an Integral Quadratic Constraints (IQC) approach has been involved. This approach is particularly interesting for two reasons. The first one is that it is possible with the same stability criterion to analyze a large class of stability problems. And the second reason is that the stability criterion is based on a frequency domain inequalities (FDI). Usually the Kalman-Yakubovich-Popov (KYP) lemma is involved to transform this infinite set of inequalities into one linear matrix inequality (LMI). But this kind of approach leads to a strong increase in the number of optimization variables. Consequently a new FDI based algorithmic approach has been developed. Usually the number of FDI to satisfy is infinite. To tackle this problem a specific technique has been developed. It consists in computing a frequency domain where the solution is valid. By an iterative approach this domain is extended until it covers [0, +∞[. In this way the solution obtained from the FDI is necessarily valid on the frequency domain continuum and the number of optimization variables remains limited which makes tractable the IQC approach for high order models.