Stability and causality constraints on frequency response coefficients applied for non-parametric H2 and H∞ control synthesis

The value of norm-based control synthesis methodologies heavily depends on the quality of the model at hand. The acquisition of low-order control oriented models however is often a non-trivial task. This paper pursuits the non-parametric synthesis of optimal controllers while omitting parametrization of the plant. As a result, the actual parametrization is performed on the controller such that no data-reduction is performed without knowledge of closed-loop relevant behavior. The synthesis of frequency response coefficients of an optimal controller for a sampled version of the mixed-sensitivity problem is considered. To convexify the problem, the actual optimization is performed over the frequency response coefficients of the Youla parameter Q_i. Using the Youla parameter, the set of stabilizing controllers is mapped onto the set of stable transfer functions. The main contribution of this paper is the derivation of algebraic constraints over Q_i that guarantee the existence of a rational stable interpolant over the points Q_i. Simulations shows that the frequency response coefficients found via the proposed approach show similar behavior as model based methods.