Robust Control Toolbox™

Uncertain matrices

Syntax

• h = umat(m) 
  

Description

Uncertain matrices are usually created by manipulation of uncertain atoms (ureal, ucomplex, ultidyn, etc.), double matrices, and other uncertain matrices. Most standard matrix manipulations are valid, including addition, multiplication, inverse, horizontal and vertical concatenation. Specific rows/columns of an uncertain matrix can be referenced and assigned also.

The command umat is rarely used. There are two situations where it may be useful. If M is a double, then H = umat(M) recasts M as an uncertain matrix (umat object) without any uncertainties. Similarly, if M is an uncertain atom, then H = umat(M) recasts M as an uncertain matrix (umat object) whose value is merely the uncertain atom. In both cases, simplify(H,'class') is the same as M.

If M is a umat, then M.NominalValue is the result obtained by replacing each uncertain atom in M with its own nominal value.

If M is a umat, then M.Uncertainty is an object describing all the uncertain atoms in M. All atoms can be referenced and their properties modified with this Uncertainty gateway. For instance, if B is an uncertain real parameter in M, then M.Uncertainty.B accesses the uncertain atom B in M.

Example

Create 3 uncertain atoms and then a 3-by-2 umat.

• a = ureal('a',5,'Range',[2 6]); 
  b = ucomplex('b',1+j,'Radius',0.5); 
  c = ureal('c',3,'Plusminus',0.4); 
  M = [a b;b*a 7;c-a b^2] 
  UMAT: 3 Rows, 2 Columns 
    a: real, nominal = 5, range = [2  6], 1 occurrence           
    b: complex, nominal = 1+1i, radius = 0.5, 4 occurrences      
    c: real, nominal = 3, variability = [-0.4  0.4], 1 occurrence 
  

View the properties of M with get

• get(M) 
      NominalValue: [3x2 double] 
       Uncertainty: [1x1 atomlist] 
  

The nominal value of M is the result when all atoms are replaced by their nominal values. View the properties of M with get

• M.NominalValue 
  ans = 
     5.0000             1.0000 + 1.0000i 
     5.0000 + 5.0000i   7.0000          
    -2.0000                  0 + 2.0000i 
  

Change the nominal value of a within M to 4. The nominal value of M reflects this change.

• M.Uncertainty.a.NominalValue = 4; 
  M.NominalValue 
  ans = 
     4.0000             1.0000 + 1.0000i 
     4.0000 + 4.0000i   7.0000          
    -1.0000                  0 + 2.0000i 
  

Get a random sample of M, obtained by taking random samples of the uncertain atoms within M.

• usample(M) 
  ans = 
     2.0072             0.8647 + 1.3854i 
     1.7358 + 2.7808i   7.0000          
     1.3829            -1.1715 + 2.3960i 
  

Select the 1st and 3rd rows, and the 2nd column of M. The result is a 2-by-1 umat, whose dependence is only on b.

• M([1 3],2) 
  UMAT: 2 Rows, 1 Columns 
    b: complex, nominal = 1+1i, radius = 0.5, 3 occurrences 
  

See Also
ureal       Creates an uncertain real parameter

ultidyn     Creates an uncertain linear time-invariant object

ucomplex    Creates an uncertain complex parameter

ucomplexm   Creates an uncertain complex matrix

usample     Generates random samples of an uncertain object

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