On the Analytic Center Cutting Plane Method for the Discrete-Time Integral Quadratic Constraint Problem

This paper applies the analytic center cutting plane method (ACCPM) to solve the discrete-time integral quadratic constraint (IQC) problem. In this problem, the constraint is expressed in terms of a frequency-domain inequality (FDI). The ACCPM is based on an oracle that identifies a feasible candidate solution satisfying the FDI for all frequencies. If the candidate solution is not feasible, the oracle returns a frequency at which the inequality is violated. The oracle for the discrete-time IQC problem is formulated in terms of a Dtype, extended symplectic matrix pencil. This paper gives an equivalent formulation to the oracle in terms of a C-type matrix pencil. C-type matrix pencils commonly appear in continuous time control problems, and so this new oracle formulation provides a link between continuous-time and discrete-time IQC problems. The C-type matrix pencil can further be modified to have a suitable skew-Hamiltonian/Hamiltonian structure, which can be exploited by structure-preserving eigensolvers to result in more accurate eigenvalue computations. The paper concludes with numerical examples showcasing the features of the ACCPM and the oracle based on the C-type matrix pencil.