Convex invertible cones and Nevanlinna-Pick interpolation: The suboptimal case

Nevanlinna-pick Interpolation: the Degenerated Case

Convex Invertible Cones, Nevalinna-Pick Interpolation and the Set of Lyapunov Solutions

For a real matrix A whose spectrum avoids the imaginary axis, it is shown that the three following, seemingly independent problems, are in fact equivalent. • Characterizing the set of real symmetric solutions of the algebraic Lyapunov inclusion associated with A. • The image of all Nevalinna-Pick interpolations associated with the spectrum of A. • The structure of the Convex Invertible Cone gen...

Nevanlinna - Pick Interpolation For

We study the Nevanlinna-Pick problem for a class of subalgebras of H∞. This class includes algebras of analytic functions on embedded disks, the algebras of finite codimension in H∞ and the algebra of bounded analytic functions on a multiply connected domain. Our approach uses a distance formula that generalizes Sarason’s [18] work. We also investigate the difference between scalar-valued and m...

Parametric Nevanlinna-Pick Interpolation Theory

We consider the robust control problem for the system with real uncertainty. This type of problem can be represented with some parameters varying between the boundaries and is formulated as parametric Nevanlinna-Pick interpolation problem in this paper. The existence of a solution for such interpolation problem depends on the positivity of the corresponding Pick matrix with elements belonging t...

Spectral Factorization and Nevanlinna - Pick Interpolation *

We develop a spectral factorization algorithm based on linear fractional transformations and on the Nevanlinna-Pick interpolation theory. The algorithm is recursive and depends on a choice of points (Zk, k 1, 2, ") inside the unit disk. Under a mild condition on the distribution of the zk's, the convergence of the algorithm is established. The algorithm is flexible and convergence can be influe...