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

Stabilization problems of linear system with right invertible constraints have mostly been solved for both global and semi-global frameworks. Linear systems subject to non-right invertible constraints have completely different characteristics compared to those with right invertible constraints. This paper addresses the control problems of linear systems subject to non-right invertible constraints. This paper also expands further the available taxonomy of constraints. The new categorization of constraints introduced reveals the difficulty in semi-global oriented control design for the non-right invertible constraints. Some new notions of stabilization are also introduced.