Before revision: Linear time-invariant distributed parameter systems Abstract evolution equations Discrete-time With U, X and Y Hilbert spaces and ∈ L(X), ∈ L(U, X), ∈ L(X, Y) and ∈ L(U, Y) the following equations determine a discrete-time linear time-invariant system: with (the state) a sequence with values in X, (the input or control) a sequence with values in U and (the output) a sequence with values in Y. Continuous-time The continuous-time case is similar to the discrete-time case but now one considers differential equations instead of difference equations: , .
After revision: differenceLinear time-invariant distributed parameter systems Abstract evolution equations Discrete-time With U, X and Y Hilbert spaces and ∈ L(X), ∈ L(U, X), ∈ L(X, Y) and ∈ L(U, Y) the following equations determine a discrete-time linear time-invariant system: with (the state) a sequence with values in X, (the input or control) a sequence with values in U and (the output) a sequence with values in Y. Continuous-time The continuous-time case is similar to the discrete-time case but now one considers differential equations instead of difference equations: , .