TY - GEN
T1 - Analysis of large scale parameter-varying systems by using scaled diagonal dominance
AU - Peni, Tamas
AU - Pfifer, Harald
PY - 2015/11/16
Y1 - 2015/11/16
N2 - It has been recognized recently that semidefinite optimization problems (SDP) can be cast into second order cone programs (SOCP) by replacing the positive definiteness constraints with stronger, scaled diagonal dominance (SDD) conditions. Since the scalability of SOCP solvers is much better than that of the SDPs, the new formulation allows solving large dimensional problems more efficiently. However, scaled diagonal dominant matrices form only a subset of the positive definite matrices. Hence, the new problem formulation results in more conservative solutions. This paper analyses the efficiency and conservativeness of the SDD formulation on two particular problems: the stability analysis and induced L2 gain computation for linear parameter-varying systems. In the paper some important features of the SDD formulation are revealed and numerical examples are provided to demonstrate the efficiency of the approach.
AB - It has been recognized recently that semidefinite optimization problems (SDP) can be cast into second order cone programs (SOCP) by replacing the positive definiteness constraints with stronger, scaled diagonal dominance (SDD) conditions. Since the scalability of SOCP solvers is much better than that of the SDPs, the new formulation allows solving large dimensional problems more efficiently. However, scaled diagonal dominant matrices form only a subset of the positive definite matrices. Hence, the new problem formulation results in more conservative solutions. This paper analyses the efficiency and conservativeness of the SDD formulation on two particular problems: the stability analysis and induced L2 gain computation for linear parameter-varying systems. In the paper some important features of the SDD formulation are revealed and numerical examples are provided to demonstrate the efficiency of the approach.
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U2 - 10.1109/ECC.2015.7331008
DO - 10.1109/ECC.2015.7331008
M3 - Conference contribution
AN - SCOPUS:84963877951
T3 - 2015 European Control Conference, ECC 2015
SP - 3091
EP - 3096
BT - 2015 European Control Conference, ECC 2015
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - European Control Conference, ECC 2015
Y2 - 15 July 2015 through 17 July 2015
ER -