A convex relaxation approach to real rational frequency domain identification

In this paper a new algorithm will be presented for parametric H_∞ frequency domain identification using convex optimization. The model to be identified is parameterized through a multivariable nominator and a scalar denominator that are affine functions of the parameter vector. This inherently nonconvex optimization problem is then rewritten as an optimization problem with coupled convex constraints and non-convex constraints. A novel convex relaxation is proposed for the non-convex constraints together with an iterative approach. Furthermore, an additional convex relaxation is proposed that provides a sensible initial guess for the iterative approach and a global lower bound for the achievable identification error. The approach is demonstrated by a simple, but illustrative example.