Forming Outputs

Any system output is some function of the state, and possibly the input (directly):

$$\underline{y}(t) \isdef o_t[\underline{x}(t),\underline{u}(t)]$$

Usually the output is a linear combination of state variables and possibly the current input:

$$\underline{y}(t) \isdefs \mathbf{C}\underline{x}(t) + \mathbf{D}\underline{u}(t)$$

where $\mathbf{C}$ and $\mathbf{D}$ are constant matrices of linear-combination coefficients