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System L1-norm

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Calculate L1-norm of impulse response of continuous-time SISO LTI system

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Calculate the L1-norm of the impulse response of a continuous-time SISO LTI system using Rutland & Lane's algorithm. A test function is included.
See Rutland N.K. & Lane P.G, "Computing the 1-norm of the impulse response of linear time-invariant systems", Systems and Control Letters, Volume 26, Number 3, pp. 211-221.

Comments and Ratings (2)


Ana (view profile)

Dear James,

Thank you for this upload, it is very useful.

The function seems to work very well for the most of the systems. However, when I try it for some higher order systems (n=24), the returned norm is an imaginary number. When the system is reduced to a smaller order, e.g. n = 10 (by using balreal), the returned norm is a positive number.

Do you have insights on why this happens and how it could be circumvented?

Thank you in advance,



Seems to work as intended. State-space input is a little inconvenient but easy to work around.



Ill conditioned systems can cause inaccurate results. A warning is included if the condition number od the A-matrix exceeds 1e6. Overcome the problem by using balreal to obtain a balanced realization.


Restriction on state-space description removed

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