Design of Hybrid Control System for Nonaffine Plants.

The purpose of this article is to develop a design method that ensures the stability of the zero-equilibrium position of a closed nonaffine control system in a certain area. The objects described by a nonlinear system of differential equations with one control and one output are considered. A constraint is introduced, which consists in the differentiability of the right-hand sides of differential equations with respect to all state variables. The task of designing control in the form of a function of the setting action, state variables and control values at previous points in time is set. This problem is solved using a quasilinear model of the control object. In the quasilinear model, matrices and vectors are functions of the variables of the state of the control object. The control is found using an algebraic polynomial matrix method. This article presents the expressions for calculating the control in accordance with the polynomial-matrix method. Based on the given coefficients of the desired polynomial, as a result of solving an algebraic system of equations, coefficients are found that are a function of control and state variables. The fulfillment of the controllability condition guarantees the existence of a solution of the specified algebraic system.