Transfer function: 1. Traditionally used method 2. Suited for single-input-single-ouput system 3. Neglect the initial condition 4. ....
State-Space:
Single-input-single-output and multi-input-multi-output systems can be formally treated equal.
The state-space representation is best suited both for the theoretical treatment of control systems (analytical solutions, optimisation) and for numerical calculations.
The determination of the system response in the homogeneous case with the initial condition is very simple.
This representation gives a better insight into the inner system behaviour. General system properties, for example, the system controllability or observability can be defined and determined.
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