Help solving Diferential Equation applied to SS System (slope as input)

Hello, I've got at State System, with "forced" inputs at bounds. My SS equation is: zp = A*z * B. (A is a square matrix, and B colunm)

If B is a step (along the time of experience), there is no problem, because I can use

tevent = 2;
tmax= 5*tevent;

n =100;
dT = n/tmax;
t = linspace(0,tmax,n);
u0 = 1 * ones(size(z'));
B = zeros(nz,n);
B(1,1)= utop(1)';
A = eye(nz,nz);
[tt,u]=ode23('SS',t,u0);

and SS is:

function zp = SS(t,z)
        global A B
        zp = A*z + B;
end

My problem is when I applied a slope (until tevent seconds) and stay in a step (until tmax), So B will be time dependent.

utop_init= 20;
utop_final = 50;
utop(1)=utop_init;
utop(tevent * dT)=utop_final;

for k = 2: tevent*dT -1
    utop(k) = utop(k-1) +(( utop(tevent * dT) - utop(1))/(tevent * dT));
end

for k = (tevent * dT) +1 :(tmax*dT)
    utop(k) = utop(k-1);
end

global A B
B = zeros(nz,1);
B(1,1:n) = utop(:)';
A = eye(nz,nz);

I wrote a new equation (to trying to solve), the problem, but I can't adjust "time step", and I don't get a u with 22x100 (which is the objective).

for k = 2 : n
u=solveSS(t,k,u0);
end

SolveSS has the code:

function [ u ] = solveSS( t,k,u0)

tspan = [t(k-1) t(k)];

[t,u] = ode15s(@SS,tspan,u0);

      function zp = SS(t,z)
          global A B
          zp = A*z + B(:,k-1);
      end

end

Thanks for the answers !