Global stabilization of classes of linear control systems with bounds on the feedback and its successive derivatives
It provides a theoretical solution for stabilizing specific linear systems with bounded feedback and its derivatives, which is an incremental contribution for control theory researchers.
The paper solves the global stabilization problem for two classes of linear systems (integrator chains and skew-symmetric systems) under constraints on the feedback amplitude and its derivatives up to order p, using nested saturations for integrator chains and a novel alternative for skew-symmetric systems, with illustrative examples.
In this paper, we address the problem of globally stabilizing a linear time-invariant (LTI) system by means of a static feedback law whose amplitude and successive time derivatives, up to a prescribed order $p$, are bounded by arbitrary prescribed values. We solve this problem for two classes of LTI systems, namely integrator chains and skew-symmetric systems with single input. For the integrator chains, the solution we propose is based on the nested saturations introduced by A.R. Teel. We show that this construction fails for skew-symmetric systems and propose an alternative feedback law. We illustrate these findings by the stabilization of the third order integrator with prescribed bounds on the feedback and its first two derivatives, and similarly for the harmonic oscillator with prescribed bounds on the feedback and its first derivative.