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For a large class of discrete-time multivariable plants with arbitrary relative degrees, the design and analysis of the direct model reference adaptive control scheme are investigated under less restrictive assumptions. The algorithm is based on a new parametrization derived from the high frequency gain matrix factorization Kp = LDU under the condition that the signs of the leading principal minors of Kp are known. By reproving the discrete-time Lp and L2δ norm relationship between inputs and outputs, establishing the properties of discrete-time adaptive law, defining the normalizing signal, and relating the signal with all signals in the closed-loop system, the stability and convergence of the discrete-time multivariable model reference adaptive control scheme are analyzed rigorously in a systematic fashion as in the continuous-time case.
For a large class of discrete-time multivariable plants with arbitrary relative degrees, the design and analysis of the direct model reference adaptive control schemes are investigated under a restrictive assumptions. The algorithm is based on a new parametrization derived from the high frequency gain matrix factorization Kp = LDU under the condition that the signs of the leading principal minors of Kp are known. By reproving the discrete-time Lp and L2δ norm relationship between inputs and outputs, establishing the properties of discrete-time adaptive law, defining the normalizing signal, and relating the signal with all signals in the closed-loop system, the stability and convergence of the discrete-time multivariable model reference adaptive control scheme are carefully rigorously in a systematic fashion as in the continuous-time case.