Robust Control Toolbox™

Create uncertain complex matrix

Syntax

• M = ucomplexm('Name',NominalValue) 
  M = ucomplexm('Name',NominalValue,'WL',WLvalue,'WR',WRvalue) 
  M = ucomplexm('Name',NominalValue,'Property',Value) 
  

Description

M = ucomplexm('Name',NominalValue) creates an uncertain complex matrix representing a ball of complex-valued matrices, centered at a NominalValue and named Name.

M = ucomplexm('Name',NominalValue,'WL',WLvalue,'WR',WRvalue) creates an uncertain complex matrix with weights WL and WR. Specifically, the values represented by M are all matrices H that satisfy norm(inv(M.WL)*(H - M.NominalValue)*inv(M.WR)) <= 1. WL and WR are square, invertible, and weighting matrices that quantify the size and shape of the ball of matrices represented by this object. The default values for WL and WR are identity matrices of appropriate dimensions.

Trailing Property/Value pairs are allowed, as in

• M = ucomplexm('NAME',nominalvalue,'P1',V1,'P2',V2,...)
  

The property AutoSimplify controls how expressions involving the uncertain matrix are simplified. Its default value is 'basic', which means elementary methods of simplification are applied as operations are completed. Other values for AutoSimplify are 'off'', no simplification performed, and 'full' which applies model-reduction-like techniques to the uncertain object.

Example

Create a ucomplexm with the name 'F', nominal value [1 2 3; 4 5 6], and weighting matrices WL = diag([.1.3]), WR = diag([.4 .8 1.2]).

• F = ucomplexm('F',[1 2 3;4 5 6],'WL',diag([.1 .3]),... 
     'WR',diag([.4 .8 1.2])); 
  

Sample the difference between the uncertain matrix and its nominal value at 80 points, yielding a 2-by-3-by-80 matrix typicaldev.

• typicaldev = usample(F-F.NominalValue,40); 
  

Plot histograms of the deviations in the (1,1) entry as well as the deviations in the (2,3) entry.

The absolute values of the (1,1) entry and the (2,3) entry are shown by histogram plots. Typical deviations in the (1,1) entry should be about 10 times smaller than the typical deviations in the (2,3) entry.

• subplot(2,1,1); 
  hist(abs(typicaldev(1,1,:)));xlim([0 .25]) 
  title('Sampled  F(1,1) - F(1,1).NominalValue') 
  subplot(2,1,2); 
  hist(abs(typicaldev(2,3,:)));xlim([0 .25]) 
  title('Sampled  F(2,3) - F(2,3).NominalValue')
  
  
  

See Also
get         Gets object properties

umat        Creates an uncertain matrix object

ucomplex    Creates an uncertain complex parameter

ultidyn     Creates an uncertain LTI dynamic object

ureal       Creates an uncertain real parameter

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