Stability analysis for a class of linear controllers under control constraints

The authors present a method for analyzing a system for stability when control magnitude constraints are introduced. They start with a given linear full state feedback controller of a certain form which stabilizes the unconstrained system. For the constrained system, where the control is obtained by saturating the linear control, stability is shown as a tradeoff between the size of the initial condition set and the size of the control constraints. As an example the linearized equations of motion for a satellite in a circular equatorial orbit are considered