State equation of finite dimensional linear systems

See:

Continuous time state equations:

Discrete time state equations:

state $\mathbf{x}(t)$ - vector of length $n \times 1$, input $\mathbf{u}(t)$ - $r \times 1$, output $\mathbf{y}(t)$ - $m \times 1$

A, B, C, D matrices, $n \times n$ , $n \times r$, $m \times n$, $m \times r$ respectively

References

1. https://crrl.poly.edu/6253/lectures/lect2.pdf