Formulation of the stability margins clearance criterion as a convex optimization problem, Report no. LiTH-ISY-R-2920

This paper presents the formulation of a flight clearance criterion as a convex optimization problem. The criterion is the stability margins criterion which is specified as an allowable phase and gain margin of a certain loop transfer function. The satisfaction of the criterion amounts to the Nichols plot of the loop transfer function being outside a specified trapezoidal region. It was shown previously that the exclusion condition from an ellipsoidal region is implied by using the generalized stability margin bPC and its calculation was performed frequency-wise by solving a sequence of convex optimization problems. In this paper we formulate the calculation of a lower bound on bPC as a convex optimization problem using Integral Quadratic Constraints (IQCs) and avoid the gridding procedure in the frequency domain. Furthermore, we formulate the problem of obtaining a lower bound on the perturbed stability margin, which is defined as the worst-case bPC over variations in real uncertain parameters.