Paper Info
Title
Characterization of the dual problem of linear matrix inequality for H-infinity output feedback control problem via facial reduction
Abstract
This paper deals with the minimization of H-infinity output feedback control. This minimization can be formulated as a linear matrix inequality (LMI) problem via a result of Iwasaki and Skelton 1994. The strict feasibility of the dual problem of such an LMI problem is a valuable property to guarantee the existence of an optimal solution of the LMI problem. If this property fails, then the LMI problem may not have any optimal solutions. Even if one can compute parameters of controllers from a computed solution of the LMI problem, then the computed H-infinity norm may be very sensitive to a small change of parameters in the controller. In other words, the non-strict feasibility of the dual tells us that the considered design problem may be poorly formulated. We reveal that the strict feasibility of the dual is closely related to invariant zeros of the given generalized plant. The facial reduction is useful in analyzing the relationship. The facial reduction is an iterative algorithm to convert a non-strictly feasible problem into a strictly feasible one. We also show that facial reduction spends only one iteration for so-called regular H-infinity output feedback control. In particular, we can obtain a strictly feasible problem by using null vectors associated with some invariant zeros. This reduction is more straightforward than the direct application of facial reduction.
Year
DOI
Venue
2020
10.1007/s00498-020-00261-z
MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS
Keywords
DocType
Volume
Linear matrix inequalities,H-infinity output feedback control,Facial reduction,Strict feasibility
Journal
32.0
Issue
ISSN
Citations 
3
0932-4194
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
Hayato Waki137628.82
Noboru Sebe236.01