Stability analysis of indirect adaptive regulation for simple discrete-time systems
离散时间系统间接自适应调节的稳定性分析

Examining adaptive regulators for a class of first-order linear discrete-time systems,with different estimators,and the modified certainty-equivalence control law,we overcome the difficulty of a loss of stability (or controllability) as the estimate of the plant gain is zero and point out a few substantive mistakes of the results from Middleton and Kokotovic's paper 1] on the corresponding continuous-time plants.We obtain the explicit expression for the phase-plane trajectories or the explicit solutions completely describing the nonlinear behavior of the designed adaptive regulating systems and analyze some problems of these adaptive regulating systems,due to a loss of stability of the estimated model.Implications of these results for the indirect adaptive regulating case of higher order linear discrete-time systems,with the unknown control direction and model parameters,are discussed.