Some complexity problems on single input double output controllers

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 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.

Original languageEnglish
Pages (from-to)1146-1158
Number of pages13
JournalDiscrete Applied Mathematics
Volume157
Issue number5
DOIs
Publication statusPublished - Mar 6 2009

Fingerprint

Controller
Controllers
Output
Graph in graph theory
State feedback
Forbidden Subgraph
Graph Classes
Search Problems
Polynomials
State Feedback
Decision problem
Time Complexity
Solvability
Polynomial time
NP-complete problem
Intersection
Partition
Sufficient
Necessary Conditions
Necessary

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

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

In: Discrete Applied Mathematics, Vol. 157, No. 5, 06.03.2009, p. 1146-1158.

Research output: Contribution to journalArticle

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