Global stabilization of linear systems with bounds on the feedback and its successive derivatives
It solves a long-standing control problem for general LTI systems with bounded input and derivative constraints, which is relevant for practical actuator limitations.
The paper proposes a static state feedback that globally stabilizes any stabilizable LTI system with bounded control input and its successive derivatives, generalizing prior results for specific system classes.
We address the global stabilization of linear time-invariant (LTI) systems when the magnitude of the control input and its successive time derivatives, up to an order $p\in\mathbb N$, are bounded by prescribed values. We propose a static state feedback that solves this problem for any admissible LTI systems, namely for stabilizable systems whose internal dynamics has no eigenvalue with positive real part. This generalizes previous work done for single-input chains of integrators and rotating dynamics.