Robust stability analysis with integral quadratic constraints (IQCs): A design example

This paper gives an overview of the applicability of the stability analysis based on integral quadratic constraints (IQCs) using the IQCbeta toolbox in MATLAB. One main advantage of the IQC theory is the possibility to deal with different kinds of perturbations - like linear time invariant (LTI) and linear time variant (LTV) parametric uncertainties, nonlinearities and unmodelled dynamics - in one stability analysis. Before using the IQCbeta toolbox the perturbated system has to be split in a nominal LTI part and the remaining parts. This step can be performed with the LFR toolbox in MATLAB, especially for large systems. In this paper a new procedure is presented how to import objects of the LFR toolbox into the IQCbeta toolbox in a general sense. As design example a controlled two-mass-spring system with friction is taken, which serves as the model for many mechanical components in real life. The main result of this paper is the stability analysis of the presented model with respect to uncertain LTI and slowly LTV parameters and nonlinearities. The stability region of the IQC analysis is compared to the one expected by extensive simulations and worst case optimizations.