Regulator problem for linear discrete-time systems with non-symmetrical constrained control

Abstract

The regulator problem is studied for linear discrete-time systems with non-symmetrical constrained control, i.e. systems described by the state equation x _k+1 = Ax _k + Bu _k, where u _k ∊ Ω, and u _k = Fx _k. Necessary and sufficient conditions allowing us to obtain the largest non-symmetrical polyhedral domain of positive invariance and contractivity with respect to motions of the system in the closed loop are established. The case of symmetrically constrained control is obtained as a particular case.