Nonlinear stability and post-critical analysis of an uncertain plant with describing functions and integral quadratic constraints

Two approaches to tackle the nonlinear robust stability problem of a plant are considered. The first employs a combination of the Describing Function method and μ analysis, while the second makes use of Integral Quadratic Constraints (IQCs). The model analyzed consists of an open-loop wing's airfoil subject to freeplay and LTI parametric uncertainties. One of the main contributions of the work is to provide methodologies to quantitatively determine the post-critical behaviour of the system, known as Limit Cycle Oscillation (LCO). When the first approach is adopted, this is studied by means of a worst-case LCO curve, whose definition is given in the paper. The IQC framework, typically used to find asymptotic stability certificates, is applied to this scenario by introducing a restricted sector bound condition for the nonlinearity.