Analytic system problems and J-lossless coprime factorization for infinite-dimensional linear systems Original Research Article

This paper extends the coprime factorization approach to the synthesis of internally stabilizing controllers satisfying an H∞-norm bound to a class of systems with irrational transfer matrices. Using the coprime factorization description, the H∞-control problem can be reduced to two stable analytic system problems. Such problems have solutions if and only if a certain J-lossless factorization exists. The full H∞-synthesis problem is shown to be equivalent to the solution of two nested J-lossless factorizations. If the irrational transfer matrix has a state-space realization, then the known state-space formulas for the H∞-control problem may be recovered using the relationship between J-lossless factorizations and solutions of Riccati equations. However, the results derived here are valid for a larger class of infinite-dimensional systems.