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special transform if matrix is unitary #619

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Jan 28, 2022
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special transform if matrix is unitary #619

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15 changes: 11 additions & 4 deletions src/matrix_comps.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -574,19 +574,26 @@ function baltrunc(sys::ST; atol = sqrt(eps()), rtol = 1e-3, n = nothing, residua
end

"""
syst = similarity_transform(sys, T)
syst = similarity_transform(sys, T; unitary=false)
Perform a similarity transform `T : Tx̃ = x` on `sys` such that
```
à = T⁻¹AT
B̃ = T⁻¹ B
C̃ = CT
D̃ = D
```

If `unitary=true`, `T` is assumed unitary and the matrix adjoint is used instead of the inverse.
"""
function similarity_transform(sys::ST, T) where ST <: AbstractStateSpace
function similarity_transform(sys::ST, T; unitary=false) where ST <: AbstractStateSpace
Tf = factorize(T)
A = Tf\sys.A*T
B = Tf\sys.B
if unitary
A = Tf'sys.A*T
B = Tf'sys.B
else
A = Tf\sys.A*T
B = Tf\sys.B
end
C = sys.C*T
D = sys.D
ST(A,B,C,D,sys.timeevol)
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