7. State and input constraints: Semi-global and global stabilization in admissible set

Chapter 4 considers internal stabilization of linear systems subject to control magnitude constraints, while Chap. 6 considers the same however with both control magnitude and rate constraints. Although such constraints on control variables occur prominently, magnitude as well as rate constraints on state variables are also of a major concern in many plants. Nearly every application imposes constraints on state as well as control variables. We observe that dynamic models of physical systems are often nonlinear. Linear approximations of such nonlinear systems are obviously valid only in certain constraint regions of state and control spaces. In process control, state and control constraints arise from economic necessity of operating the plants near the boundaries of feasible regions. In connection with safety issues, state and control constraints are a major concern in many plants. In certain possibly hazardous systems, such as a nuclear power plant, safety limits on some variables are often imposed. The violations of such predetermined safety measures may cause system malfunction or even damage. This implies that magnitude constraints or bounds on states must be taken as integral parts of any control system design.