Nehari Problem for Infinite-Dimensional Linear Systems of Parabolic Type

摘要

A complete solution is obtained to the suboptimal Nehari extension problem fortransfer functions of parabolic systems with Dirichlet boundary control and smooth observations. The solutions are given in terms of the realization (A,B,C), where A is a uniformly strongly elliptic operator of order two with smooth coefficients, B = AB(sub D) and B(sub D) is the Dirichlet map associated with Dirichlet boundary conditions and C is a bounded observation map from L(sub 2)(Omega) to the output space Y. A is defined on the bounded open domain Omega of R(sup d). The approach is to solve an equivalent J-spectral factorization problem for this particular realization.