The linear time invariant system is represented by the state space model as
\(\frac{dX}{dt} = A X + B U \)
\(Y = CX + DU\)
Consider n=number of state variables, m = number of inputs, p= number of outputs. The state transition matrix Φ( t) Φ( t) is given by:
1
Φ(t) = [(SI-A)]-1
2
Φ(t) = L-1 [(SI-A)]-1
3
Φ(t) = L[(SI-A)]-1
4
Φ(t) = L-1 [(SI-A)]