TY - GEN
T1 - H2 norm of linear time-periodic systems
T2 - 2006 American Control Conference
AU - Jovanović, Mihailo R.
PY - 2006/1/1
Y1 - 2006/1/1
N2 - We consider a class of linear time-periodic systems in which dynamical generator A(t) represents a sum of a stable time-invariant operator A 0 and a small amplitude zero-mean T-periodic operator εA p(t). We employ a perturbation analysis to develop a computationally efficient method for determination of the H2 norm. Up to a second order in perturbation parameter SL we show that: a) the H2 norm can be obtained from a conveniently coupled system of readily solvable Lyapunov and Sylvester equations; b) there is no coupling between different harmonics of Ap(t) in the expression for the H2 norm. These two properties do not hold for arbitrary values of , and their derivation would not be possible if we tried to determine the H2 norm directly without resorting to perturbation analysis. Our method is well suited for identification of the values of period T that lead to the largest increase/reduction of the H2 norm. Two examples are provided to motivate the developments and illustrate the procedure.
AB - We consider a class of linear time-periodic systems in which dynamical generator A(t) represents a sum of a stable time-invariant operator A 0 and a small amplitude zero-mean T-periodic operator εA p(t). We employ a perturbation analysis to develop a computationally efficient method for determination of the H2 norm. Up to a second order in perturbation parameter SL we show that: a) the H2 norm can be obtained from a conveniently coupled system of readily solvable Lyapunov and Sylvester equations; b) there is no coupling between different harmonics of Ap(t) in the expression for the H2 norm. These two properties do not hold for arbitrary values of , and their derivation would not be possible if we tried to determine the H2 norm directly without resorting to perturbation analysis. Our method is well suited for identification of the values of period T that lead to the largest increase/reduction of the H2 norm. Two examples are provided to motivate the developments and illustrate the procedure.
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U2 - 10.1109/acc.2006.1656422
DO - 10.1109/acc.2006.1656422
M3 - Conference contribution
AN - SCOPUS:34047211980
SN - 1424402107
SN - 9781424402106
T3 - Proceedings of the American Control Conference
SP - 1452
EP - 1457
BT - Proceedings of the 2006 American Control Conference
PB - Institute of Electrical and Electronics Engineers Inc.
Y2 - 14 June 2006 through 16 June 2006
ER -