System analysis via integral quadratic constraints

System Analysis via Integral Quadratic Constraints

This paper introduces a unified approach to robustness analysis with respect to nonlinearities, time variations, and uncertain parameters. From an original idea by Yakubovich, the approach has been developed under a combination of influences from the Western and Russian traditions of control theory. It is shown how a complex system can be described, using integral quadratic constraints (IQC’s) ...

Exponential Stability Analysis via Integral Quadratic Constraints

The theory of integral quadratic constraints (IQCs) allows verification of stability and gain-bound properties of systems containing nonlinear or uncertain elements. Gain bounds often imply exponential stability, but it can be challenging to compute useful numerical bounds on the exponential decay rate. This work presents a generalization of the classical IQC results of Megretski and Rantzer [1...

Analysis and Design of Optimization Algorithms via Integral Quadratic Constraints

This manuscript develops a new framework to analyze and design iterative optimization algorithms built on the notion of Integral Quadratic Constraints (IQC) from robust control theory. IQCs provide sufficient conditions for the stability of complicated interconnected systems, and these conditions can be checked by semidefinite programming. We discuss how to adapt IQC theory to study optimizatio...

Friction Analysis Based on Integral Quadratic Constraints

Integral Quadratic Constraints

Integral Quadratic Constraints (IQC) are inequalities used to describe (partially) possible signal combinations within a given dynamical system. IQC offer a framework for abstracting ”challenging” (e.g. non-linear, time-varying, uncertain, or distributed) elements of dynamical system models to aid in rigorous analysis of robust stability and performance (more specifically, to establish L2 gain ...