RTITR(G)

NAME
rtitr - discrete time response (transfer matrix)

CALLING SEQUENCE
[y]=rtitr(Num,Den,u [,up,yp])

PARAMETERS

Num,Den
    : polynomial matrices (resp. dimensions : nxm and nxn)

u   : real matrix (dimension mx(t+1)

up,yp
    : real matrices (dimension m x (maxi(degree(Den))) (default values=0)

y   : real matrix

DESCRIPTION
y=rtitr(Num,Den,u [,up,yp]) returns the time response of the discrete time linear system with transfer matrix Den^-1 Num for the input u, i.e y and u are such that Den y = Num u at t=0,1,...

If d1=maxi(degree(Den)), and d2=maxi(degree(Num)) the polynomial matrices Den(z) and Num(z) may be written respectively as:
  D(z)= D_0  + D_1  z + ... + D_d1   z^d1
  N(z)= N_0  + N_1  z + ... + N_d2   z^d2
and Den y = Num u is interpreted as the recursion:
  D(0)y(t)+D(1)y(t+1)+...+ D(d1)y(t+d1)= N(0) u(t) +....+ N(d2) u(t+d2)
The columns of u are the inputs of the system at t=0,1,...,T:
  u=[u(0) , u(1),...,u(T)]
The outputs at t=0,1,...,T+d1-d2 are the columns of the matrix y:
  y=[y(0), y(1),  .... y(t+d1-d2)]
up and yp define the initial conditions for t < 0 i.e
  up=[u(-d1), ..., u(-1)  ]
  yp=[y(-d2), ...  y(-1)  ]
The default values of up and yp are zero: up = 0*ones(m,d1), yp=0*ones(n,d2)

EXAMPLE
z=poly(0,'z');
Num=1+z;Den=1+z;u=[1,2,3,4,5];
rtitr(Num,Den,u)-u

SEE ALSO
ltitr, exp, flts.