Forming Outputs

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

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

The general case of output extraction is shown in Fig.1.5.

Figure 1.5: Continuous-time state-space model with output vector $\underline {y}(t) = o_t[\underline {x}(t),\underline {u}(t)]$ .

The output signal (vector) is most typically a linear combination of state variables and possibly the current input:

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

where $C$ and $D$ are constant matrices of linear-combination coefficients.