Optimal Estimation of the Linear Functional of State Variables of a Dynamic System

The paper considers the problem of building an observer that ensures optimal estimation of the linear functional of state variables of a dynamic system. In addition, the degree of influence of unknown initial conditions on the integral error of observation in the absence of an external disturbance (the level of initial disturbance rejection in the system) acts as a minimized criterion. It is shown that when a number of constraints are fulfilled, an observer can be used to solve the problem posed, the order of which is equal to the order of the estimated functional. The conditions for the existence of such an observer is determined, the linear matrix inequalities, the solution of which allows one to determine its matrix coefficients are formulated.