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Abstract. Over the last several years a new theory of Nevanlinna-Pick interpolation with complexity constraint has been developed for scalar interpolants. In this paper we generalize this theory to the matrix-valued case, also allowing for multiple interpolation points. We parameterize a class of interpolants consisting of "most interpolants" of no higher degree than the central solution in terms of spectral zeros. This is a complete parameterization, and for each choice of interpolant we provide a convex optimization problem for determining it. This is derived in the context of duality theory of mathematical programming. To solve the convex optimization problem, we employ a homotopy continuation technique previously developed for the scalar case. These results can be applied to many classes of engineering problems, and, to illustrate this, we provide some examples. In particular, we apply our method to a benchmark problem in multivariate robust control. By constructing a controller satisfying all design specifications but having only half the McMillan degree of conventional H ∞ controllers, we demonstrate the efficiency of our method.

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This paper presents an application of gain-scheduling (GS) control techniques to a floating offshore wind turbine on a barge platform for above rated wind speed cases. Special emphasis is placed on the dynamics variation of the wind turbine system caused by plant nonlinearity with respect to wind speed. The turbine system with the dynamics variation is represented by a linear parameter-varying (LPV) model, which is derived by interpolating linearized models at various operating wind speeds. To achieve control objectives of regulating power capture and minimizing platform motions, both linear quadratic regulator (LQR) GS and LPV GS controller design techniques are explored. The designed controllers are evaluated in simulations with the NREL 5 MW wind turbine model, and compared with the baseline proportional-integral (PI) GS controller and non-GS controllers. The simulation results demonstrate the performance superiority of LQR GS and LPV GS controllers, as well as the performance trade-off between power regulation and platform movement reduction.