The paper presents the results of the development of standard algorithms for the design of stabilization systems for uncertain dynamic objects and for the design of control systems with limited data on the state of the object. New algorithms have been formulated to improve the robustness of the state vector estimation process for control objects against uncertainty factors. These algorithms differ from existing ones in that they allow the regularization of the task of creating algorithms for estimating controller parameters within adaptive control systems with an adaptive model. The study presents and evaluates some of the most effective algorithms for computing pseudoinverse matrices. To determine the pseudoinverse matrix of a control object, it uses modified QR decomposition algorithms, adapted by adding or removing a column, together with robust algorithms for inverting a non-singular block matrix while identifying its left and right zero divisors of maximum rank. The resulting algorithms suggest that stabilization systems can be constructed using a local optimization approach, even when relying on approximate mathematical models.