TY - GEN

T1 - Constructing a sequence of relaxation problems for robustness analysis of uncertain LTI systems via dual LMIs

AU - Matsuda, Yusuke

AU - Ebihara, Yoshio

AU - Hagiwara, Tomomichi

PY - 2009/12/1

Y1 - 2009/12/1

N2 - This paper gives a new procedure for robustness analysis of linear time-invariant (LTI) systems whose state space coefficient matrices depend polynomially on multivariate uncertain parameters. By means of dual linear matrix inequalities (LMIs) that characterize performance of certain LTI systems, we firstly reduce these analysis problems into polynomial matrix inequality (PMI) problems. However, these PMI problems are non-convex and hence computationally intractable in general. To get around this difficulty, we construct a sequence of LMI relaxation problems via a simple idea of linearization. In addition, we derive a rank condition on the LMI solution under which the exactness of the analysis result is guaranteed. From the LMI solution satisfying the rank condition, we can easily extract the worst case parameters.

AB - This paper gives a new procedure for robustness analysis of linear time-invariant (LTI) systems whose state space coefficient matrices depend polynomially on multivariate uncertain parameters. By means of dual linear matrix inequalities (LMIs) that characterize performance of certain LTI systems, we firstly reduce these analysis problems into polynomial matrix inequality (PMI) problems. However, these PMI problems are non-convex and hence computationally intractable in general. To get around this difficulty, we construct a sequence of LMI relaxation problems via a simple idea of linearization. In addition, we derive a rank condition on the LMI solution under which the exactness of the analysis result is guaranteed. From the LMI solution satisfying the rank condition, we can easily extract the worst case parameters.

UR - http://www.scopus.com/inward/record.url?scp=77950806342&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77950806342&partnerID=8YFLogxK

U2 - 10.1109/CDC.2009.5399826

DO - 10.1109/CDC.2009.5399826

M3 - Conference contribution

AN - SCOPUS:77950806342

SN - 9781424438716

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 2174

EP - 2179

BT - Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009

T2 - 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009

Y2 - 15 December 2009 through 18 December 2009

ER -