In this article there has been conducted analysis of Lyapunov matrix application in order to form control inputs under different dynamic systems’ optimization methods oriented by quadratic integral criterion. For this purpose, the methods of finding the Lyapunov matrix and optimization based on the Bellman functional equation with subsequent application of the Riccati equation, optimization taking into account the initial values of state variables, optimization based on the Bellman equation using linear matrix inequalities and Lyapunov equation are considered. Despite the complexity of solving the Riccati equation, the problem of finding the Lyapunov matrix is unambiguous only in the case of application of optimization methods based on dynamic Bellman programming and representation of the Bellman function by the Lyapunov function. Optimization based on the application of the linear matrix inequality condition is not unambiguous, as it requires the choice of the inequality solution. The optimization of the system by the integral quadratic criterion and the initial values of the state variables is also ambiguous because there is a problem of solving nonlinear interconnected optimization equations.
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