Stability of non-linear QFT designs based on robust absolute stability criteria

The paper is mainly devoted to the robust stability problem of non-linear Q FT designs. The problem is first formulated for SISO non-linear systems, li mited in practice to linear-memoryless sector-bounded nan-linear interconne ctions, and in an I/O stability sense. The work investigates several possib le robust adaptations of the Circle Criterion, depending on the type of res ulting interconnection of linear and non-linear blocks, appearing in the fe edback system. Also, the use of the Popov Criterion is investigated as an a lternative less conservative than the Circle Criterion in some cases. The p roposed techniques are given in usual QFT language, expressed as frequency conditions or boundaries in the Nichols Chart, allowing an easy integration with other design objectives. In addition, multivariable extensions using a conicity condition and the concept of maximal cone are adopted to give st ability boundaries in interconnections of SIMO linear-MISO sector-bounded m emoryless blocks. All the robust stability criteria are illustrated using s ignificant examples to emphasize the practical application of the resulting techniques.