Mapping integral quadratic constraints into parameter space

This paper presents the mapping equations for integral quadratic constraints (IQCs). In particular it is shown that IQCs with bounded rational multipliers can be mapped into parameter space. Using IQCs not only provides a uniform framework to map specifications into parameter space, but provides a unified approach to parameter space based robustness analysis and synthesis with respect to nonlinearities, time variations, and uncertain parameters. The exploitation of additional degrees of freedom contained in the multipliers is also addressed. To this end convex optimization problems in terms of linear matrix inequalities (LMIs) can be formulated and solved during the mapping process.