Structure and factorization of quadratic constraints for robustness analysis

This paper extends and generalizes the preliminary results of Goh and Safonov (1995), linking the integral quadratic constraint (IQC) approach for robust analysis to previous work on generalized sectors, dissipativity and J-spectral factorization/indefinite scalar products. The emphasis is on the factorization theory associated with the fact that IQCs for robust analysis must have a J-spectral factorization ∫ _-∞^∞z^*S^* (ω)diag(I,-I)S(ω)z dω. In particular, we prove the existence of bounded and invertible conic sector type factorizations of the IQC, and also of certain rank and Riccati equation type restrictions on LMI based IQC-analysis methods. The implications of our results for the robustness analysis of systems with structured uncertainty are also clarified