# setDelayModel

Construct state-space model with internal delays

## Syntax

sys = setDelayModel(H,tau)
sys = setDelayModel(A,B1,B2,C1,C2,D11,D12,D21,D22,tau)

## Description

sys = setDelayModel(H,tau) constructs the state-space model sys obtained by LFT interconnection of the state-space model H with the vector of internal delays tau, as shown:

sys = setDelayModel(A,B1,B2,C1,C2,D11,D12,D21,D22,tau) constructs the state-space model sys described by the following equations:

$\begin{array}{c}\frac{dx\left(t\right)}{dt}=Ax\left(t\right)+{B}_{1}u\left(t\right)+{B}_{2}w\left(t\right)\\ y\left(t\right)={C}_{1}x\left(t\right)+{D}_{11}u\left(t\right)+{D}_{12}w\left(t\right)\\ z\left(t\right)={C}_{2}x\left(t\right)+{D}_{21}u\left(t\right)+{D}_{22}w\left(t\right)\\ w\left(t\right)=z\left(t-\tau \right).\end{array}$

tau (τ) is the vector of internal delays in sys.

## Input Arguments

 H State-space (ss) model to interconnect with internal delays tau. tau Vector of internal delays of sys. For continuous-time models, express tau in seconds. For discrete-time models, express tau as integer values that represent multiples of the sample time. A,B1,B2,C1,C2,D11,D12,D21,D22 Set of state-space matrices that, with the internal delay vector tau, explicitly describe the state-space model sys.

## Output Arguments

 sys State-space (ss) model with internal delays tau.

## Tips

• setDelayModel is an advanced operation and is not the natural way to construct models with internal delays. See Time Delays in Linear Systems for recommended ways of creating internal delays.

• The syntax sys = setDelayModel(A,B1,B2,C1,C2,D11,D12,D21,D22,tau) constructs a continuous-time model. You can construct the discrete-time model described by the state-space equations

$\begin{array}{c}x\left[k+1\right]=Ax\left[k\right]+{B}_{1}u\left[k\right]+{B}_{2}w\left[k\right]\\ y\left[k\right]={C}_{1}x\left[k\right]+{D}_{11}u\left[k\right]+{D}_{12}w\left[k\right]\\ z\left[k\right]={C}_{2}x\left[k\right]+{D}_{21}u\left[k\right]+{D}_{22}w\left[k\right]\\ w\left[k\right]=z\left[k-\tau \right].\end{array}$

To do so, first construct sys using sys = setDelayModel(A,B1,B2,C1,C2,D11,D12,D21,D22,tau). Then, use sys.Ts to set the sample time.

## Version History

Introduced in R2007a