Convergence of stochastic gradient estimation algorithm for multivariable ARX-like systems

This paper studies the convergence of the stochastic gradient identification algorithm of multi-input multi-output ARX-like systems (i.e., multivariable ARX-like systems) by using the stochastic martingale theory. This ARX-like model contains a characteristic polynomial and differs from the conventional multivariable ARX system. The results indicate that the parameter estimation errors converge to zero under the persistent excitation conditions. The simulation results validate the proposed convergence theorem.