Some Complexity Problems on Single Input Double Output Controllers

Katalin M. Hangos, Zsolt Tuza, Anders Yeo
2001 BRICS Report Series  
<p>We investigate the time complexity of constructing single input<br />double output state feedback controller structures, given the <br />directed structure graph G of a system. Such a controller structure<br />defines a restricted type of P3-partition of the graph G. A necessary<br /> condition (*) has been found and two classes of graphs have<br />been identified where the search problem of finding a feasible P3-<br />partition is polynomially solvable and, in addition, (*) is not only<br
more » ... necessary but also sufficient for the existence of a P3-partition. It<br />is shown further that the decision problem on two particular graph<br />classes - defined in terms of forbidden subgraphs - remains NP-<br />complete, but is polynomially solvable on the intersection of those<br />two classes. Moreover, for every natural number m, a stabilizing<br />structure with Single Input m-Output controllers can be found in<br />polynomial time for the system in question, if it admits one.</p>
doi:10.7146/brics.v8i18.20475 fatcat:vvjvh4b7t5aizhrc7ualm7q36q