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In this paper, we address the problem of globally stabilizing a lineartime-invariant (LTI) system by means of a static feedback law whose amplitudeand successive time derivatives, up to a prescribed order $p$, are bounded byarbitrary prescribed values. We solve this problem for two classes of LTIsystems, namely integrator chains and skew-symmetric systems with single input.For the integrator chains, the solution we propose is based on the nestedsaturations introduced by A.R. Teel. We show that this construction fails forskew-symmetric systems and propose an alternative feedback law. We illustratethese findings by the stabilization of the third order integrator withprescribed bounds on the feedback and its first two derivatives, and similarlyfor the harmonic oscillator with prescribed bounds on the feedback and itsfirst derivative.

Global stabilization of classes of linear control systems with bounds on the feedback and its successive derivatives