TY - GEN
T1 - Theoretical analysis of balanced truncation for linear switched systems
AU - Petreczky, Mihaly
AU - Wisniewski, Rafal
AU - Leth, John-Josef
PY - 2012
Y1 - 2012
N2 - In this paper we present theoretical analysis of model reduction of linear switched systems based on balanced truncation, presented in [1,2]. More precisely, (1) we provide a bound on the estimation error using L2 gain, (2) we provide a system theoretic interpretation of grammians and their singular values, (3) we show that the singular values of grammians depend only on the input-output map and not on the choice of the state-space representation. In addition, we also show that quadratic stability and LMI estimates of the L2 gain also depend only on the input-output map. The main tool for showing this independence is realization theory of linear switched systems. [1] H. R. Shaker and R. Wisniewski, "Generalized gramian framework for model/controller order reduction of switched systems", International Journal of Systems Science, Vol. 42, Issue 8, 2011, 1277-1291. [2] H. R. Shaker and R. Wisniewski, "Switched Systems Reduction Framework Based on Convex Combination of Generalized Gramians", Journal of Control Science and Engineering, 2009.
AB - In this paper we present theoretical analysis of model reduction of linear switched systems based on balanced truncation, presented in [1,2]. More precisely, (1) we provide a bound on the estimation error using L2 gain, (2) we provide a system theoretic interpretation of grammians and their singular values, (3) we show that the singular values of grammians depend only on the input-output map and not on the choice of the state-space representation. In addition, we also show that quadratic stability and LMI estimates of the L2 gain also depend only on the input-output map. The main tool for showing this independence is realization theory of linear switched systems. [1] H. R. Shaker and R. Wisniewski, "Generalized gramian framework for model/controller order reduction of switched systems", International Journal of Systems Science, Vol. 42, Issue 8, 2011, 1277-1291. [2] H. R. Shaker and R. Wisniewski, "Switched Systems Reduction Framework Based on Convex Combination of Generalized Gramians", Journal of Control Science and Engineering, 2009.
UR - http://www.scopus.com/inward/record.url?scp=84866087821&partnerID=8YFLogxK
U2 - 10.3182/20120606-3-NL-3011.00039
DO - 10.3182/20120606-3-NL-3011.00039
M3 - Article in proceeding
SN - 978-3-902823-00-7
T3 - I F A C Workshop Series
SP - 240
EP - 247
BT - 4th IFAC Conference on Analysis and Design of Hybrid Systems, 2012
PB - IFAC Publisher
T2 - 4th IFAC Conference on Analysis and Design of Hybrid Systems
Y2 - 6 June 2012 through 8 June 2012
ER -