A convex approach to generalized fixed order interpolation

In this paper, we address the problem of finding a fixed order plant that interpolates given data in time and frequency domain, and satisfies additional constraints such as stability and passivity. The comprehensive framework developed in this paper can be used to address a wide range of complex control problems such as system identification with a priori bound on its order, fixed-order controller design and spectral estimation. To solve the proposed interpolation problem, it is first shown that it can be recast as finding a point in a properly defined semi-algebraic set. Then, an efficient numerical algorithm based on convex relaxations of rank minimization is proposed to solve the problem. Numerical examples are provided to illustrate the efficiency of the algorithm.