THE CONDITIONS OF CONSTRUCTING OF THE ALMOST CONSERVATIVE SYSTEM USING CONTROLLING VECTOR - Svyatovets, I. F. (Computer Science and Applied Mathematics, 2016)
This article describes a fully controlled linear discrete system with a small parameter. The coefficient matrix of the variable is of the form 0 1 F  F where ε -is the small parameter. The system is not almost conservative, i.e., matrix 0 F is not an orthogonal matrix. To obtain an almost conservative system is constructed linear static state feedback, which is the sum of two terms. After substituting the control vector in the original system, a closed system is obtained. It uses the approach that, first we construct the necessary matrix coefficients, and then calculate the feedback vector. The theorem formulated shows that the coefficient matrix of open and closed systems are linked by the least squares method. It was obtained the conditions on the elements of the matrix 0 F , to produce the desired orthogonal matrix, if the matrix at control is known. An example of the transition to almost conservative system by using of feedback is shown with constructing the optimal controller of the obtained system. It uses the approach, which proposes an asymptotic expansion on the small parameter of the solution of matrix Riccati equation. To find an approximate solution we use an infinite system of matrix equations that are solved using mathematical computer algebra system Maple V. It is shown that a given system by constructing optimal controller up to the first order is stabilized.