A nonlinear standard problem

A nonlinear standard problem involving conic/sector nonlinearities is studied from the point of view of stability and sensitivity. The author makes use of intervals of a sector and defines for nonlinear relations induced norms, sum of vectors, multiplication of a sector by a scalar, and the composition product of two sectors. He addresses the following problem: given a plant H₁ and a feedback H₂, find conditions on H₂ that guarantee both stability and sensitivity performance, i.e., find the penalty on the sector of relation H₂ which guarantees a given sensitivity upper bound. The more general framework of the standard problem is addressed to derive general conditions for both stability and sensitivity performance. Extensions to the multivariable case are considered which detail the method of analysis allowing sensitivity considerations