Analytic system problems and \(J\)-lossless coprime factorization for infinite-dimensional linear systems
Let \(G\in H_\infty\) be given; the following problem is considered: Find all \(Q_1,Q_2\in H_\infty\) such that \[ \left[\begin{matrix} R\\ I\end{matrix}\right]= \left[\begin{matrix} G_{11} &G_{12}\\ G_{21} & G_{12}\end{matrix}\right]\left[\begin{matrix} Q_1\\ Q_2\end{matrix}\right],\quad|R|_\infty<\gamma. \] The approach is the one in [\textit{M. Green}, SIAM J. Control Optimization 30, 522-547 (1992; Zbl 0756.93039)]; consisting in the equivalence to a \(J\)-spectral factorization problem. This approach gives at the matrix-transfer level a solution to both the discrete-time and the continuous-time case. The stable analytic problem is solved for transfer matrices with an impulse response \(h\) satisfying \[ \int^\infty_0 e^{\varepsilon t}|h(t)|dt<\infty. \] All the details of proofs are included in an internal report of the authors: Analytic system problems and \(J\)-lossless coprime factorization of infinite-dimensional systems, Rep. W-9218, Mathematics Inst., Univ. of Groningen, The Netherlands.
scientific article; zbMATH DE number 1011321
scientific article