delayss

Create state-space models with delayed inputs, outputs, and states

Syntax

sys=delayss(A,B,C,D,delayterms) sys=delayss(A,B,C,D,ts,delayterms)

Description

sys=delayss(A,B,C,D,delayterms)constructs a continuous-time state-space model of the form:

$\begin{array}{l} \frac{d x}{d t} = A x (t) + B u (t) + \sum_{j = 1}^{N} (A j x (t - t j) + B j u (t - t j)) \\ y (t) = C x (t) + D u (t) + \sum_{j = 1}^{N} (C j x (t - t j) + D j u (t - t j)) \end{array}$

where t_j, j=1,..,N are time delays expressed in seconds. delayterms is a struct array with fields delay, a, b, c, d where the fields of delayterms(j) contain the values of tj, Aj, Bj, Cj, and Dj, respectively. The resulting model sys is a state-space (SS) model with internal delays.

sys=delayss(A,B,C,D,ts,delayterms)constructs the discrete-time counterpart:

$\begin{array}{l} x [k + 1] = A x [k] + B u [k] + \sum_{j = 1}^{N} {A j x [k - n j] + B j u [k - n j]} \\ y [k] = C x [k] + D u [k] + \sum_{j = 1}^{N} {C j x [k - n j] + D j u [k - n j]} \end{array}$

where Nj, j=1,..,N are time delays expressed as integer multiples of the sample time ts.

Examples

To create the model:

$\begin{array}{l} \frac{d x}{d t} = x (t) - x (t - 1.2) + 2 u (t - 0.5) \\ y (t) = x (t - 0.5) + u (t) \end{array}$

type

DelayT(1) = struct('delay',0.5,'a',0,'b',2,'c',1,'d',0);
DelayT(2) = struct('delay',1.2,'a',-1,'b',0,'c',0,'d',0);
sys = delayss(1,0,0,1,DelayT) 

a = 
       x1
   x1   0
 
b = 
       u1
   x1   2
 
c = 
       x1
   y1   1
 
d = 
       u1
   y1   1
 
(values computed with all internal delays set to zero)

Internal delays: 0.5  0.5  1.2  
 
Continuous-time model.

Version History

Introduced in R2007a

delayss

Syntax

Description

Examples

Version History

See Also