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An analytical comparison between the nonsingular quadratic performance of robust and adaptive backstepping designs

Robust and adaptive backstepping designs for an uncertain strict feedback system are compared with respect to a cost functional which is based on an instantaneous quadratic penalty measuring both the output transient and the control effort. It is shown that the adaptive design outperforms the robust design when the actual uncertainty level is sufficiently high and the a-priori known uncertainty level is sufficiently conservative.