Semi-global stabilization of discrete-time systems subject to non-right invertible constraints

This paper investigates time-invariant linear systems subject to input and state constraints. We study discrete-time systems with full or partial constraints on both input and state. It has been shown earlier that the solvability conditions of stabilization problems are closely related to important concepts such as the right invertibility or non-right invertibility of the constraints, the location of constraint invariant zeros, and the order of constraint infinite zeros. In this paper, for general time-invariant linear systems with non-right invertible constraints, necessary and sufficient conditions are developed under which semi-global stabilization in the admissible set can be achieved by state feedback. Sufficient conditions are also developed for such a stabilization in the case where measurement feedback is used. Such sufficient conditions are almost necessary. Controllers for both state feedback and measurement feedback are constructed as well.