Stability and optimality of robust stochastic multivariable self-tuning tracker

This paper considers properties of Astrom-Wittenmark´s self tuning tracker for MIMO systems described with the ARX model. It is supposed that the stochastic noise has the non-Gaussian distribution. Consequence of that fact is nonlinear transformation of tracking error in the direct adaptive minimum variance controller. System under consideration is minimum phase with different dimensions for input and output vectors. Using concept of Kronecker product it is possible to represent unknown parameters in the form of vector, so the tensor calculus is avoided. Global stability is proved without any modification of matrix gain in the recursive algorithm. Also, the assumption about the absolutely continuous finite-dimensional distributions and different modification of high frequency gain is discussed