Semi-global stabilization and output regulation of constrained linear plants via measurement feedback

Systems with state and input constraints are prevalent in the practice of control engineering. Most of the research during the past ten years focused on the systems with input constraints. The research activities during this time can broadly be divided into two directions. The first direction follows the so-called a priori design philosophy in which all the constraints are taken into account right at the onset of analysis and design. The second direction follows the so called a posteriori design philosophy. In this philosophy, initially all the constraints are ignored and a satisfactory design method is used to to meet the design goals in the absence of constraints. Subsequent to this, an additional feedback layer is designed to insure stability and to reduce the loss of performance due the presence of constraints compared to the performance of the originally designed controller. Anti-windup design methodology belongs to this second category. In addition to input constraints, state constraints also widely exist in practical control systems. Although some research activity has appeared in the literature dealing with state constraints, little attention has been paid to the structural properties associated to the constraints. Recently a new approach to state and input constraints has appeared, where the constraints on the state and/or input are modeled by a constrained output [5, 8]. In [5, 8], for the first time, in the presence of state and input constraints, both stabilization and output regulation problems in a global framework as well as a semiglobal framework are formulated. Solvability conditions for such problems are developed, and whenever the solvability conditions are satisfied, explicit design methodologies to arrive at appropriate controllers or regulators are presented. The work done in [5, 8] focuses only on utilizing state feedback. For state feedback, and for the case of right invertible constraints, the results developed in [5, 8] are complete and deal with different facets of global and semi-global stabilization and output regulation. Results for non-right invertible constraints are yet to be developed.