Abstract
The aim of this paper is to develop a synthesis method for a self organizing control system for linear objects with m-inputs and n-outputs within the class of two-parameter structurally stable mappings. The proposed approach is based on the gradient-velocity method of Lyapunov vector functions. Conditions for aperiodic robust stability of stationary states are derived in the form of systems of parametric inequalities that define admissible regions of parameter variations. It is shown that transitions between stable states may occur due to bifurcations, which are interpreted as a manifestation of self-organization. A procedure for selecting a self-organizing model with prescribed transient characteristics is developed, along with a method for computing controller coefficients based on matching the stability conditions of the model and the control system. The scientific novelty of the work lies in the development of a unified synthesis framework that ensures aperiodic transient responses, robustness under parameter uncertainty, and suppression of oscillatory and chaotic regimes. Keywords: self-organization, MIMO systems, bifurcation, Lyapunov method, robust stability, structurally stable mappings.