Some complexity problems on single input double output controllers

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1 Citation (Scopus)


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
Issue number5
Publication statusPublished - Mar 6 2009


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

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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