The Linear Constrained Control Problem for Discrete-Time Systems: Regulation on the Boundaries

Abstract

The chapter deals with the problem of regulation of linear systems around an equilibrium lying on the boundary of a polyhedral domain where linear constraints on the control and/or the state vectors are satisfied. In the first part of the chapter, the fundamental limitations for constrained control with active constraints at equilibrium are exposed. Next, based on the invariance properties of polyhedral and semi-ellipsoidal sets, design methods for guaranteeing convergence to the equilibrium while respecting linear control constraints are proposed. To this end, Lyapunov-like polyhedral functions, LMI methods and eigenstructure assignment techniques are applied.