State Transformation

Applies a "state transformation" to a given rational matrix \(K(z) = C(Iz^{-1} - A)^{-1}B +D\) in statespace form. The parameter matrices are transformed as \(A \rightarrow T A T^{-1}\), \(B \rightarrow T B\) and \(C \rightarrow C T^{-1}\), where \(T\) is a non-singular (square) matrix.

Usage

state_trafo(obj, T, inverse = FALSE)

Arguments

obj

stsp object, represents a rational matrix \(K(z)\).

T

state transformation matrix. The parameter T must be a non-singular (s-by-s) matrix, or a vector of length s^2 (in this case T is coerced to an s-by-s matrix) or a vector of length s. In the latter case T is coerced to a diagonal s-by-s matrix.

inverse

if TRUE, the transformation is reversed, i.e. \(A \rightarrow T^{-1} A T\), \(B \rightarrow T^{-1} B\) and \(C \rightarrow C T\).

Value

stsp object which represents the transformed state space realization.

Examples

obj = stsp(A = c(0,0.2,1,-0.5),
           B = c(1,1), C = c(1,0))
           
# random state transformation
T = stats::rnorm(4)
obj1 = state_trafo(obj, T)

# obj and obj1 are equivalent, they produce the same IRF
testthat::expect_equivalent(pseries(obj), pseries(obj1))

# diagonal state transformation matrix
T = stats::rnorm(2)
obj1 = state_trafo(obj, T)

# revert the transformation
testthat::expect_equivalent(obj, state_trafo(obj1, T, inverse = TRUE))
if (FALSE) {
state_trafo(obj, stats::rnorm(9)) # dimension of T does not fit
state_trafo(obj, c(1,0))          # T = diag(c(1,0)) is singular!
}