Abstract
This paper establishes a.s. global convergence of the implicit self-tuning controller (STC) based on the least squares method for a SISO discrete linear stochastic system with colored disturbance and containing the general time-delay. The most extensive treatment of the problem of global convergence appears in the work of Ljung, but a question which concerns the boundedness of the system variables remains unanswered. To overcome this, the equivalent stochastic feedback system associated with the error equations of the STC is shown, and using a martingale convergence theorem and a strictly positive realness, its conditions for a.s. convergence are revealed. From the result, it is found for the STC that, with probability one, the STC scheme ensures under suitable conditions the system input and output are sample mean square bounded and the conditional mean square of a posteriori error achieves its minimum possible value. The results of this paper develop that studied by Ljung in respect to the general time-delay, weighting identification and a.s. global convergence. Fur thermore, it is shown that there is no necessity for monitoring the boundedness of the system variables in this analysis.
