EECS20N: Signals and Systems

Vector-valued LCCDE Systems

An N-dimensional LCCDE system is of the form: ∀ n ≥ 0,

s(n + 1) = As(n) + Bx(n),

y(n) = Cs (n) + Dx(n)

where at reaction n,

  • s(n) ∈ RealsN is the state,
  • x(n) ∈ RealsM is the input, and
  • y(n)∈ RealsK is the output.

The coefficients in the equations are:

  • A is a constant N × N matrix,
  • B is a constant N × M matrix,
  • C is a constant K × N matrix, and
  • D is a constant K × M matrix.

If s(0) = 0, then this describes an LTI system.