There are many different ways to represent any physical system, differential equations, transfer function, state space... Since they all represent the same physical system, there must be ways to transform from one to another. This document has links to individual pages describing these transformations.

In many cases when transforming from one representation to another, an easier
alternative is to go through an intermediate representation. For example when
changing from a single n^{th} order differential equation to a state space
representation (1DE↔SS) it is easier to do from the differential equation to a transfer
function representation, then from transfer function to state space (1DE↔TF followed
by TF↔SS).

The "Printable" link (above) links to a page that has all of these transformations.

Transformation |
Alternative |
Description |

CDE → 1DE | Coupled Differential Equation to Single Differential Equation | |

1DE ↔ TF | Single Differential Equation to/from Transfer Function | |

1DE ↔ SS | 1DE ↔ TF; TF ↔ SS | Single Differential Equation to/from State Space |

1DE ↔ PZ | 1DE ↔ TF; TF ↔ PZ | Single Differential Equation to/from Pole Zero |

1DE ↔ SFG | 1DE ↔ TF; TF ↔ SS; SS ↔ SFG | Single Differential Equation to/from Signal Flow Graph |

TF ↔ SS | Transfer Function to/from State Space | |

TF ↔ PZ | Transfer Function to/from Pole Zero | |

TF ↔ SFG | TF ↔ SS; SS ↔ SFG | Transfer Function to/from Signal Flow Graph |

SS ↔ SS | State Space to/from State Space | |

SS ↔ PZ | SS ↔ TF; TF ↔ PZ | State Space to/from Pole Zero (note: SS↔TF is same as TF↔SS) |

SS ↔ SFG | State Space to/from Signal Flow Graph | |

PZ ↔ SFG | PZ ↔ TF; TF ↔ SS; SS ↔ SFG | Pole Zero to/from Signal Flow Graph (note: PZ↔TF is same as TF↔PZ) |

© Copyright 2005 to 2014 Erik Cheever This page may be freely used for educational purposes.

Erik Cheever Department of Engineering Swarthmore College© Copyright 2005 to 2014 Erik Cheever This page may be freely used for educational purposes.

Erik Cheever Department of Engineering Swarthmore College