## 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. 