### Abstract

We investigate the time complexity of constructing single input double output state feedback controller structures, given the directed structure graph G of a system. Such a controller structure defines a restricted type of P_{3}-partition of the graph G. A necessary condition (*) is described and some classes of graphs are identified where the search problem of finding a feasible P_{3}-partition is polynomially solvable and, in addition, (*) is not only necessary but also sufficient for the existence of a P_{3}-partition. It is also proved that the decision problem on two particular graph classes - defined in terms of forbidden subgraphs - remains NP-complete, but is polynomially solvable on the intersection of those two classes. The polynomial-time solvability of some further related problems is shown, too.

Original language | English |
---|---|

Pages (from-to) | 1146-1158 |

Number of pages | 13 |

Journal | Discrete Applied Mathematics |

Volume | 157 |

Issue number | 5 |

DOIs | |

Publication status | Published - Mar 6 2009 |

### Keywords

- Directed graph
- Hall condition
- P-factor
- Polynomial algorithm
- State feedback controller
- Structural process control

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics

## Fingerprint Dive into the research topics of 'Some complexity problems on single input double output controllers'. Together they form a unique fingerprint.

## Cite this

*Discrete Applied Mathematics*,

*157*(5), 1146-1158. https://doi.org/10.1016/j.dam.2008.03.028