Create uncertain matrix
M = umat(A)
Uncertain matrices are rational expressions involving uncertain elements of type ureal, ucomplex, or ucomplexm. Use uncertain matrices for worst-case gain analysis and for building uncertain state-space (uss) models.
Create uncertain matrices by creating uncertain elements and combining them using arithmetic and matrix operations. For example:
p = ureal('p',1); M = [0 p; 1 p^2]
creates a 2-by-2 uncertain matrix (a umat object) with the uncertain parameter p.
The syntax M = umat(A) converts the double array A to a umat object with no uncertainty.
Most standard matrix manipulations are valid on uncertain matrices, including addition, multiplication, inverse, horizontal and vertical concatenation. Specific rows/columns of an uncertain matrix can be referenced and assigned also.
If M is a umat, then M.NominalValue is the result obtained by replacing each uncertain element in M with its own nominal value.
If M is a umat, then M.Uncertainty is an object describing all the uncertain elements in M. All element 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 element B in M.
Create 3 uncertain elements 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]
M is an uncertain matrix (umat object) with the uncertain parameters a, b, and c.
View the properties of M with get
The nominal value of M is the result when all atoms are replaced by their nominal values.
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.