A REDUCED-ORDER FRAMEWORK APPLIED TO LINEAR-SYSTEMS WITH CONSTRAINED CONTROLS

A major issue in the control of dynamical systems is the integration o f both technological constraints and some dynamic performance requirem ents in the design of the control system. We show in this work that it is possible to solve a class of constrained control problems of linea r systems by using a reduced-order system obtained by the projection o f the trajectories of the original system onto a subspace associated w ith the undesirable open-loop eigenvalues. The class of regulation sch emes considered uses full state feedback to guarantee that any traject ory emanating from a given polyhedral set of admissible initial states remains in that set. This set of admissible states is said to be posi tively invariant with respect to the closed-loop system. We also addre ss the important issues of numerical stability and complexity of the c omputations.