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 -