This is an irrational transfer function. The best way to implement it would be to create a MATLAB function with 's', the complex frequency as input argument and output the numeric value of transfer function.
Something like the following would do:
function out = Gfcn(s)
out = (-s*exp(-0.1*s) + 1 - exp(-0.1*s))/(s + exp(-0.1*s) - 1);
end
This function can then be called repeatedly for obtaining the required system characteristics.
Else you can create a transfer function by using pade approximation for transport delays. One simple way will be the following:
s = tf('s');
G = (-s*exp(-0.1*s) + 1 - exp(-0.1*s))/(s + exp(-0.1*s) - 1); % This creates a state space model for your system
Ga = pade(G,2); % Make a rational system using pade approximation for transport delay
[den, num] = ss2tf(Ga.a, Ga.b, Ga.c, Ga.d); % Obtain numerator and denominator of pade approximated system
Gtf = tf(num, den) %Transfer function of system with time delays approximated using pade approximation
