Some complexity problems on single input double output controllers

  • Authors:

  • K. M. Hangos;Zs. Tuza;A. Yeo

  • Affiliations:

  • Computer and Automation Institute, Hungarian Academy of Sciences, H-1111 Budapest, Kende u. 13-17, Hungary;Computer and Automation Institute, Hungarian Academy of Sciences, H-1111 Budapest, Kende u. 13-17, Hungary and Department of Computer Science, University of Pannonia, H-8200 Veszprém, Egyetem ...;Department of Computer Science, Royal Holloway, University of London, Egham, Surrey TW20 0EX, United Kingdom

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2009

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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.