Abstract
All-coefficient adaptive control theory and method based on characteristic models have already been applied successfully in the fields of astronautics and industry. However, the stability analysis of the characteristic model-based golden-section adaptive control systems is still an open question in both theory and practice. To investigate such stability issues, the author first provides a method for choosing initial parameter values and new performances for a projection algorithm with dead zone for adaptive parameter estimation, and develops some properties of time-varying matrices by utilizing some algebraic techniques. And then a new Lyapunov function with logarithmic form for time-varying discrete systems is constructed. Finally, the author transforms the characteristic models of some multi-input and multi-output (MIMO) controlled systems into their equivalent form, and proves the stability of the closed-loop systems formed by the golden-section adaptive control law based on the characteristic model using mathematical techniques.
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