Invariant Set Solution in Matlab

Hi,

I want to solve the following problem in matlab

if true

 % sigma is a 2X4 matrix.
 % x is a 4X1 matrix [x1, x2, x3, x4]'. These are my states in a system.
 % B is a 4X2 matrix.
 % Note: * is matrix multiplications
 %       ' means transpose of a matrix
 % S = sigma' * x(t)

 % co-effs of sigma meet the following conditions
  % 1. sigma' * x(t)=0;
  % 2. sigma' * x(t) is an invariant set.
  % 3. If S != 0 then S*Sdot < 0 for all t,x.
  % 4. sigma' * B is a non-singular matrix.

end

I want to find out sigma and subsequently the function S = sigma' * x(t) Thanks.