Compute LTI model norms
computes the or norm of a continuous- or discrete-time LTI model.
The norm of a stable continuous system with transfer function , is the root-mean-square of its impulse response, or equivalently
The infinity norm is the peak gain of the frequency response, that is,
where denotes the largest singular value of a matrix.
The discrete-time counterpart is
norm(sys,2) both return the norm of the TF, SS, or ZPK model
sys. This norm is infinite in the following cases:
sysis continuous and has a nonzero feedthrough (that is, nonzero gain at the frequency ).
norm(sys) produces the same result as
norm(sys,inf) computes the infinity norm of any type of LTI model
sys. This norm is infinite if
sys has poles on the imaginary axis in continuous time, or on the unit circle in discrete time.
norm(sys,inf,tol) sets the desired relative accuracy on the computed infinity norm (the default value is
[ninf,fpeak] = norm(sys,inf) also returns the frequency
fpeak where the gain achieves its peak value.
Consider the discrete-time transfer function
with sample time 0.1 second. Compute its norm by typing
Compute its infinity norm by typing
These values are confirmed by the Bode plot of .
The gain indeed peaks at approximately 3 rad/sec and its peak value in dB is found by typing
norm uses the same algorithm as
covar for the norm, and the algorithm of  for the infinity norm.
sys is first converted to state space.
Frequency response computation
Singular value plot
 Bruisma, N.A. and M. Steinbuch, "A Fast Algorithm to Compute the -Norm of a Transfer Function Matrix," System Control Letters, 14 (1990), pp. 287-293.