Paper Info
Title
A Simultaneous Balanced Truncation Approach to Model Reduction of Switched Linear Systems.
Abstract
This paper deals with model reduction by balanced truncation of switched linear systems (SLS). We consider switched linear systems whose dynamics, depending on the switching signal, switches between finitely many linear systems with a common state space. These linear systems are called the modes of the SLS. The idea is to seek for conditions under which there exists a single state space transformation that brings all modes of the SLS in balanced coordinates. As a measure of reachability and observability of the state components of the SLS, we take the average of the diagonal gramians. We then perform balanced truncation by discarding the state components corresponding to the smallest diagonal elements of this average balanced gramian. In order to carry out this program, we derive necessary and sufficient conditions under which a finite collection of linear systems with common state space can be balanced by a single state space transformation. Among other things, we derive sufficient conditions under which global uniform exponential stability of the SLS is preserved under simultaneous balanced truncation. Likewise, we derive conditions for preservation of positive realness or bounded realness of the SLS. Finally, in case that the conditions for simultaneous balancing do not hold, or we simply do not want to check these conditions, we propose to compute a suitable state space transformation on the basis of minimization of an overall cost function associated with the modes of the SLS. We show that in case our conditions do hold, this transformation is in fact simultaneously balancing, bringing us back to the original method described in this paper.
Year
DOI
Venue
2012
10.1109/TAC.2012.2202031
IEEE Trans. Automat. Contr.
Keywords
DocType
Volume
Symmetric matrices,Linear systems,Switches,Eigenvalues and eigenfunctions,Reduced order systems,Stability analysis,Matrix decomposition
Journal
57
Issue
ISSN
Citations 
12
0018-9286
9
PageRank 
References 
Authors
0.59
8
3
Name
Order
Citations
PageRank
Nima Monshizadeh116216.85
Harry L. Trentelman215922.15
M. K. Camlibel325324.88