### 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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Applied Mathematics
- Discrete Mathematics and Combinatorics

### Cite this

*Discrete Applied Mathematics*,

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

**Some complexity problems on single input double output controllers.** / Hangos, K.; Tuza, Z.; Yeo, A.

Research output: Contribution to journal › Article

*Discrete Applied Mathematics*, vol. 157, no. 5, pp. 1146-1158. https://doi.org/10.1016/j.dam.2008.03.028

}

TY - JOUR

T1 - Some complexity problems on single input double output controllers

AU - Hangos, K.

AU - Tuza, Z.

AU - Yeo, A.

PY - 2009/3/6

Y1 - 2009/3/6

N2 - 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 P3-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 P3-partition is polynomially solvable and, in addition, (*) is not only necessary but also sufficient for the existence of a P3-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.

AB - 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 P3-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 P3-partition is polynomially solvable and, in addition, (*) is not only necessary but also sufficient for the existence of a P3-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.

KW - Directed graph

KW - Hall condition

KW - P-factor

KW - Polynomial algorithm

KW - State feedback controller

KW - Structural process control

UR - http://www.scopus.com/inward/record.url?scp=60949090209&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=60949090209&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2008.03.028

DO - 10.1016/j.dam.2008.03.028

M3 - Article

VL - 157

SP - 1146

EP - 1158

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

IS - 5

ER -