IQC analysis and synthesis via nonsmooth optimization

Abstract

Integral quadratic constraints (IQCs) are used in system theory to model nonlinear phenomena within the framework of linear feedback control. IQC theory addresses parametric robustness, saturation effects, sector nonlinearities, passivity, and much else. In IQC analysis specially structured linear matrix inequalities (LMIs) arise and are currently addressed by structure exploiting LMI solvers. Controller synthesis under IQC constraints is nonconvex and much harder and has been attempted sporadically by global optimization techniques such as branch and bound, cutting plane or D - K -type coordinate descent ideas. Here, we revisit IQC theory and propose a completely different algorithmic solution based on local and nonsmooth optimization methods. This is less ambitious than global methods, but is very promising in practice. Our approach, while aiming high at IQC synthesis, offers new answers even for IQC analysis, because we optimize without Lyapunov variables. For high-order systems this leads to a significant reduction of the number of unknowns.