Stability Analysis by a New Algorithmic Approach Based on Integral Quadratic Constraints: Application to an Aircraft Benchmark

Auteurs: 

F. Demourant (ONERA)

To analyze a non-linear, uncertain and time-varying closed loop representing a fighter aircraft model interconnected with a control law, an Integral Quadratic Constraint (IQC) approach has been used. 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. The second reason is that the stability criterion is based on frequency dependent inequalities (FDI). Usually, the Kalman-Yakubovich-Popov (KYP) lemma is used, in order to transform this infinite set of inequalities into one linear matrix inequality (LMI). However, this kind of approach leads to a steep increase in the number of optimization variables. Consequently, a new FDIbased algorithmic approach has been developed. Usually, the number of FDI that must be satisfied is infinite or, thanks to a frequency domain gridding, it is possible to avoid this problem but with the drawback of not being able to guarantee the validity of the solution throughout the frequency domain continuum. 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 to cover [0,+∞[. Thus, the solution obtained from the FDI is necessarily valid throughout the frequency domain continuum and the number of optimization variables remains limited, which makes the IQC approach tractable for high-order models.

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