20.1 INTRODUCTION

---

- 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.

example,

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.