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System L1-norm

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System L1-norm



01 May 2013 (Updated )

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.

Required Products Control System Toolbox
MATLAB release MATLAB 8.2 (R2013b)
MATLAB Search Path
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Comments and Ratings (2)
03 Nov 2014 Ana

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,


03 Oct 2014 Timothy

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

06 Oct 2014 1.3

Restriction on state-space description removed

12 Nov 2014 1.4

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.

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