Journal article

Computing the L-2 gain for linear periodic continuous-time systems

Michael Cantoni, Henrik Sandberg



A method to compute the L2 gain is developed for the class of linear periodic continuous-time systems that admit a finite-dimensional state-space realisation. A bisection search for the smallest upper bound on the gain is employed, where at each step an equivalent discrete-time problem is considered via the well-known technique of time-domain lifting. The equivalent problem involves testing a bound on the gain of a linear shift-invariant discrete-time system, with the same state dimension as the periodic continuous-time system. It is shown that a state-space realisation of the discrete-time system can be constructed from point solutions to a linear differential equation and two differential ..

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Awarded by Australian Research Council

Funding Acknowledgements

This paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Associate Editor Yoshito Ohta under the direction of Editor Roberto Tempo. This work was supported in part by the Australian Research Council (DP0664225) and the Swedish Foundation for Strategic Research.