Effectiveness of state constraints in controllability and least squares optimal control problem

Controllability of linear time-invariant systems with linear state variable inequality constraints is studied using a Lyapunov approach. Sufficient conditions for controllability, are obtained, and classes of admissible controls are defined such that the state trajectories remain inside a given open region in state space. These controls may take the form of least squares optimal state feedback control laws. In such cases the unconstrained optimal golutions satisfy the state constraints, and the constraints become inactive.