The regulator problem for linear discrete-time systems with nonsymmetrical constrained control

Abstract

The author considers the regulator problem for linear discrete-time systems described by the equations x/sub k+1/=Ax/sub k/+Bu/sub k/, where u/sub k/=Fx/sub k/ epsilon Omega , and Omega is a nonsymmetrical polyhedral set. A necessary and sufficient condition ensuring that all the motions of the system emanating from the set F/sup -1/ Omega remain in this set is given. The asymptotic stability of the origin is also guaranteed.<>