Robust Stability Analysis with Integral Quadratic Constraints (IQCs): A Design Example

Abstract

This paper gives an overview of the applicability of the stability analysis based on integral quadratic constrainds (IQCs) using the IQCβ toolbox in MATLAB. One main advantage of teh IQC theory is the possibility to deal with different kinds of perturbations - like linear time invariant (LTI) and lineaer time variant (LTV) parametric uncertainties, nonlinearities and unmodelled dynamics - in one stability analysis. Before using the IQCβ toolbox the perturbated system has to be split in a nominal LTI part and the remaining parts. this step can be performed with the LFT toolbox in MATLAB, especially for large systems. In this paper a new procedure is presented how to import objects of the LFT toolbox into the IQCβ 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 LFT and slolly LTV parameters and nonlinearities. The stability region of the IQC analysis is compared to the one expected by extensive simulations and worst case optimizations.