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For a class of discrete-time systems,the design and analysis of direct model reference adaptive control(MRAC)with normalized adaptive law are investigated.We reprove the discrete-time conclusions on the(?)_p and(?)_(2δ)relationship properties between the input and the output,and the discrete-time swapping Lemmas 1 and 2.We also establish the properties of discrete-time adaptive law,define the normalizing signal,and relate the signal with all the signals in the closed-loop system.Thus,the stability and convergence properties of the discrete-time MRAC scheme are analyzed rigorously in a systematic fashion as in the continuous-time case.
For a class of discrete-time systems, the design and analysis of direct model reference adaptive control (MRAC) with normalized adaptive law are investigated. We reprove the discrete-time conclusions on the (?) _ P and (?) _ (2δ) relationship properties between the input and the output, and the discrete-time swapping Lemmas 1 and 2. We also establish the properties of discrete-time adaptive law, define the normalizing signal, and relate the signal with all the signals in the closed-loop system.Thus, the stability and convergence properties of the discrete-time MRAC scheme are carefully rigorously in a systematic fashion as in the continuous-time case.