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getdelaymodel - State-space representation of internal delays

Syntax

[A,B1,B2,C1,C2,D11,D12,D21,D22,E,tau] = getdelaymodel(sys,'mat')
[H,tau] = getdelaymodel(sys,'lft')

Description

[A,B1,B2,C1,C2,D11,D12,D21,D22,E,tau] = getdelaymodel(sys,'mat') returns the matrices A,B1,B2, etc. and vector tau of internal delays for the state-space model sys . The E matrix is set to [] for explicit models with no E matrix.

State-space models with internal delays are represented by differential-algebraic equations of the form:

E dx/dt = A x + B1 u + B2 w

y = C1 x + D11 u + D12 w

z = C2 x + D21 u + D22 w

w(t) = z(t − tau)

or their discrete-time counterparts:

E x[k+1] = A x[k] + B1 u[k] + B2 w[k]

y[k] = C1 x[k] + D11 u[k] + D12 w[k]

z[k] = C2 x[k] + D21 u[k] + D22 w[k]

w[k] = z[k − tau]

where u,y are the external inputs and outputs, and tau is the vector of internal delays. These equations correspond to this block diagram:

where H(s) is the delay-free state-space model mapping [u;w] to [y;z].

[H,tau] = getdelaymodel(sys,'lft') returns the state-space model H and vector tau of internal delays making up the block diagram above.

Note that for models without internal delays:

• Only A,B1,C1,D11 (and possibly E) are non-empty

• tau is empty and H is equal to sys.

See Also

delayss, dss, ss, setdelaymodel

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