2009/01/25 by Ian Gravagne, John M. Davis, Gravagne, Ian A. +3 · 1 citation
Engineering · Mathematics · #93C25 #93C40 #FOS: Mathematics #Nonlinear Differential Equations Analysis #Numerical methods for differential equations #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.0901.3873
openalex publication_date 2009/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It has been known for some time that proportional output feedback will stabilize MIMO, minimum-phase, linear time-invariant systems if the feedback gain is sufficiently large. High-gain adaptive controllers achieve stability by automatically driving up the feedback gain monotonically. More recently, it was demonstrated that sample-and-hold implementations of the high-gain adaptive controller also require adaptation of the sampling rate. In this paper, we use recent advances in the mathematical field of dynamic equations on time scales to unify and generalize the discrete and continuous versions of the high-gain adaptive controller. We prove the stability of high-gain adaptive controllers on a wide class of time scales.