Transfer Function Models
Corresponding to each linear state space equation in the time domain with input u(t) and output y(t) is a matrix of transfer functions relating the Laplace tranforms of the input, U(s) to that of the output, Y(s). The transfer function matrix consists of (scalar) elements g_{ij}(s). For example if there are three inputs ( ie U(s) is of size 3×1 ) and there are four outputs ( ie Y(s) is of size 4×1 ) the transfer function matrix has the form