- state equations can be converted to transfer functions. The derivation follows.
- state equation coefficient matrices can be transformed to another equivalent for, if the state vector is rearranged.
• The transfer function form can be put into a matrix form. In this case the denominator is the characteristic equation.
• The free (homogeneous) response of a system can be used to find the state transition matrix.
• The forced response (particular) response of the system can be found using convolution,
• As an example the homogeneous/free response of the system is shown below.
• The forced/particular solution is shown below,
• If a matrix is diagonizable, the diagonal matrix can be found with the following technique. This can be used for more advanced analysis techniques to create diagonal (and separable) system matrices.
• If there are repeated Eigenvalues in the system the Jordan Form can be used.
• The Eigenvectors can be used to calculate the system response.
• zeros of state space functions can be found using the state matrices.
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