Paper Info
Title
Optimal Control on the Doubly Infinite Continuous Time Axis and Coprime Factorizations.
Abstract
We study the problem of existence of weak right or left or strong coprime factorizations in H-infinity over the right half-plane of an analytic function defined in some subset of the right half-plane. We give necessary and sufficient conditions for the existence of such coprime factorizations in terms of an optimal control problem over the doubly infinite continuous time axis. In particular, we show that an equivalent condition for the existence of a strong coprime factorization is that both the control and the filter algebraic Riccati equation (of an arbitrary realization that need not be well-posed) have a solution (in general unbounded and not even densely defined) and that a coupling condition involving these two solutions is satisfied. The proofs that we give are partly based on corresponding discrete time results which we have recently obtained.
Year
DOI
Venue
2014
10.1137/110831726
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
Keywords
Field
DocType
Riccati equation,linear quadratic optimal control,infinite-dimensional system,coprime factorization,input-output stabilization,state feedback
Discrete mathematics,Mathematical optimization,Coupling,Optimal control,Analytic function,Mathematical proof,Riccati equation,Algebraic Riccati equation,Discrete time and continuous time,Coprime integers,Mathematics
Journal
Volume
Issue
ISSN
52
3
0363-0129
Citations 
PageRank 
References 
0
0.34
4
Authors
2
Name
Order
Citations
PageRank
Mark R. Opmeer18715.71
Olof J. Staffans26615.08