Conic sector analysis using integral quadratic constraints

Abstract

Summary This paper interprets the Conic Sector stability results of Zames, and the multivariable generalizations provided by Safonov and Athans, in an integral quadratic constraint context. The ideas are formulated for the case where one element of a feedback interconnection is linear and the other satisfies a conic sector condition. This scenario allows the main stability results to be formulated using integral quadratic constraints, with all finite‐sector cases being captured using this framework. The stability results are expressed using frequency domain inequalities or linear‐matrix inequalities. Some examples show how the main technical result can, in the multivariable case, be used to provide a reduction in conservatism over standard results.

Zames-Falb Multipliers: don't panic

“…Previously, at this point, positivity of h(t) was invoked, but suppose this is not assumed; instead use will be made of the other version of the area inequality -inequality (20). From equation (33) it follows that…”