Attempting to take the z transform of a continuous transform function

I am fairly new to matlab and simulink, having been able to get away by not using it so far. However at this stage I need to use it to derive the discrete-time system of the function,

where

I have a basic understand on needing to using code simular to this

clear all
clc

%% model the system
G1 = tf('s')
(22.5,[4*1 4*0.9 4*9]);

%% compute z trasnform
Ts = 0.1;
G_z = c2d(G1,Ts,'foh');

How I am unsure on how to implement the exp?

Any assistance will be greatly appreciated.

[Star Strider]

This seems to be a homework problem. See also: How do you add a multiplication in the numerator of a transfer function.

Answer 1

[Dyuman Joshi]

tau = 1;
sys = tf(5,[1 5],'InputDelay',tau)

sys =
 
                5
  exp(-1*s) * -----
              s + 5
 
Continuous-time transfer function.

Alternate way

s = tf('s');
G = exp(-tau*s)/(s+5)

G =
 
                1
  exp(-1*s) * -----
              s + 5
 
Continuous-time transfer function.