Calculating system bandwidth using Function "bandwidth"

Hi,

I need to calculate the bandwidth of a SISO system. For that there is a function bandwidth(sys,drop) in control toolbox. But MATLAB has also another built-in function with the same name which returns the lower and upper bandwidth of a matrix.

How can I specifically use the function from control toolbox?

Does MATLAB automatically distinguish between these two functions based on my inputs?

The descriptions of these two are as following:

"

%BANDWIDTH  Computes the frequency response bandwidth.
%
%   FB = BANDWIDTH(SYS) returns the bandwidth FB of the SISO dynamic
%   system SYS, defined as the first frequency where the gain drops below
%   70.79 percent (-3 dB) of its DC value. The frequency FB is expressed
%   in rad/TimeUnit (relative to the time units specified in SYS.TimeUnit,
%   the default being seconds). For FRD models, BANDWIDTH uses the first
%   frequency point to approximate the DC gain.
%
%   FB = BANDWIDTH(SYS,DBDROP) further specifies the critical gain drop
%   in dB. The default value is -3 dB or a 70.79 percent drop.
%
%   If SYS is an array of dynamic systems, BANDWIDTH returns an array FB
%   of the same size where FB(k) = BANDWIDTH(SYS(:,:,k)).
%
%   See also DCGAIN, ISSISO, DYNAMICSYSTEM.

%   Copyright 1986-2011 The MathWorks, Inc.

"

"

%BANDWIDTH returns the lower and upper bandwidth of a matrix.
%   [LOWER,UPPER] = BANDWIDTH(X) returns the lower bandwidth LOWER, and the upper 
%   bandwidth UPPER of matrix X.
%   
%   LOWER = BANDWIDTH(X,'lower') returns the lower bandwidth LOWER of matrix X.
% 
%   UPPER = BANDWIDTH(X,'upper') returns the upper bandwidth UPPER of matrix X.
% 
%   See also ISBANDED, ISDIAG, ISTRIL, ISTRIU.

%   Copyright 2013 The MathWorks, Inc.
%   Built-in function.

"

Thank you

.

Answer 1

[Sam Chak]

Hi @Alireza Aghdaei

The function can distinguish from the input type. One requires a Dynamic System Model, the other requires a Matrix.

% Example 1
sys = tf(1, [1 1])

sys =
 
    1
  -----
  s + 1
 
Continuous-time transfer function.

fb  = bandwidth(sys)

fb = 0.9976

% Example 2
B = tril(magic(5))

B = 5×5

17 0 0 0 0 23 5 0 0 0 4 6 13 0 0 10 12 19 21 0 11 18 25 2 9

[lower, upper] = bandwidth(B)

lower = 4

upper = 0

[Steven Lord]

You can confirm this using the which function.

% Example 1
sys = tf(1, [1 1]);
which bandwidth(sys) % Control System Toolbox bandwidth

/MATLAB/toolbox/control/ctrlanalysis/@DynamicSystem/bandwidth.m  % tf method

% Example 2
B = tril(magic(5));
which bandwidth(B) % MATLAB bandwidth

built-in (/MATLAB/toolbox/matlab/matfun/bandwidth)