Question
Given the state-equation of a linear system as
x·(t) = Ax(t) + Bu(t)
with u(t) = constant for KT ≤ t ≤ (k+1)T.
The system is discretised resulting in the following discrete-time equation:
X[(k +1)T] = Φ (T)X(kT) + θ (T)u(kT)
if
find the matrices Φ (T) and θ (T).