Contents I. Introduction
The synthesis of a self-tuning control system requires the completion of the following steps: identification of a linear model for process and the exogenous signals that act over it, choose the control objectives and the cost function that will be minimized, selection of the synthesis procedure according to the process model and the adopted performance criterion, implementation of the self-tuning control algorithm, analyze the convergence and stability of control system [1]. The subject of this paper is focused on the last step presented. As initial premises there are considered some aspects regarding the process model, respectively the self-tuning control strategies. Assuming the input sequence and respectively the output sequence the following discrete linear model can be considered for the controlled process: $$A(z^{-1})y(t)=z^{-k}B(z^{-1})u(t)\eqno{\hbox{(1)}}$$ where $$\eqalignno{&A(z^{-1})=1+a_{1}z^{-1}+a_{2}z^{-2}+\ldots+a_{n}z^{-n}\cr &B(z^{-1})=b_{0}+b_{1}z^{-1}+b_{2}z^{-2}+\ldots+b_{m}z^{-m}}$$ are stable polynomials (-one sample time delay operator).
