Computing the 1-norm of the impulse response of linear time-invariant systems

Lower and upper bounds to the 1-norm of the impulse response of linear time-invariant systems are derived. It is shown that the bounds can be adjusted so that the difference between them is arbitrarily small. An algorithm is described that uses the bounds to compute the 1-norm of the impulse response to a pre-specified tolerance. Details are given of how to compute the bounds for state-space systems. Finally, two numerical examples of using the algorithm are given.

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