ANALYTIC SYSTEM PROBLEMS AND J-LOSSLESS COPRIME FACTORIZATION FOR INFINITE-DIMENSIONAL LINEAR SYSTEMS

摘要

This paper extends the coprime factorization approach to the synthesis of internally stabilizing controllers satisfying an H-infinity-norm bound to a class of systems with irrational transfer matrices. Using the coprime factorization description, the H-infinity-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-infinity-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-infinity-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. (C) Elsevier Science Inc., 1997. [References: 51]