17th International Symposium on
Mathematical Theory of Networks and Systems
Kyoto International Conference Hall, Kyoto, Japan, July 24-28, 2006

MTNS 2006 Paper Abstract

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Paper FrP01.2

Karlsson, Johan (Royal Inst. of Tech. (KTH)), Lindquist, Anders (Royal Inst. of Tech.)

On degree-constrained analytic interpolation with interpolation points close to the boundary

Scheduled for presentation during the Regular Session "H2 and H-infinity Control II" (FrP01), Friday, July 28, 2006, 15:45−16:10, Room B2

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on March 28, 2024

Keywords H2/H-infinity, L1 control, Convex optimization

Abstract

In the recent article a paradigm for complexity constrained interpolation of contractive functions is developed. In particular, it is shown that any such interpolant may be obtained from a convex optimization problem, minimizing a generalized entropy gain. With this as a background, we study the optimization problem in detail and derive certain properties of it. One of the main results is that, if, for a sequence of interpolants, the values of the generalized entropy gain of the interpolants converge to the optimum, then the interpolants converge in H_2. This result is used in order to get the asymptotic behavior of the interpolant as an interpolation point approach the boundary of the domain of analyticity. Finally, a control design example which has been considered by Nagamune is studied, and the results are reexamined in this framework.