TY - GEN

T1 - Closed form expressions for linear MIMO system responses and solutions of the Lyapunov equation

AU - Hauksdóttir, Anna Soffía

AU - Sigurosson, Sven Th

AU - Aoalgeirsson, Sigurour Örn

AU - Herjólfsson, Gísli

PY - 2007

Y1 - 2007

N2 - In this paper, closed form expressions of linear MIMO system responses are presented. These expressions make use of matrix polynomial formulations of etA. They depend on the eigenvalues of A, the characteristic polynomial of A, as well as the partial fraction expansion coefficients of the corresponding unity numerator transfer function. The general partial fraction coefficients may be calculated using a computationally efficient recursive formula that has been derived in the context of SISO system responses. The final expressions are presented in a form that enhances the understanding of linear systems as such and emphasizes efficient computational implementation and the resulting time complexity. Finally, a closed form solution of the Lypunov equation, the Gramian, is presented.

AB - In this paper, closed form expressions of linear MIMO system responses are presented. These expressions make use of matrix polynomial formulations of etA. They depend on the eigenvalues of A, the characteristic polynomial of A, as well as the partial fraction expansion coefficients of the corresponding unity numerator transfer function. The general partial fraction coefficients may be calculated using a computationally efficient recursive formula that has been derived in the context of SISO system responses. The final expressions are presented in a form that enhances the understanding of linear systems as such and emphasizes efficient computational implementation and the resulting time complexity. Finally, a closed form solution of the Lypunov equation, the Gramian, is presented.

KW - Gramian

KW - Linear continuous time MIMO system responses

KW - Lyapunov equation

KW - Matrix exponential

KW - Partial fraction expansion coefficients

UR - http://www.scopus.com/inward/record.url?scp=52449121863&partnerID=8YFLogxK

U2 - 10.1109/CDC.2007.4434159

DO - 10.1109/CDC.2007.4434159

M3 - Conference contribution

AN - SCOPUS:52449121863

SN - 1424414989

SN - 9781424414987

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 2797

EP - 2802

BT - Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC

T2 - 46th IEEE Conference on Decision and Control 2007, CDC

Y2 - 12 December 2007 through 14 December 2007

ER -