Direct model reference adaptive control using K p = LDU factorization for multivariable discrete-time plants

Abstract

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 ofKp are known. By reproving the discrete-time \( \mathcal{L}_p \) and \( \mathcal{L}_{2\delta } \) 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.