The rationale for the need for continuous monitoring of such an indicator of power quality as the level of harmonic components is given. An approach to the design of harmonic network filters and a method of monitoring their level in the supplied electricity with the definition of the source of their occurrence and increase is proposed.

In this paper, we study 3-dimensional stationary flows of real gases described by Euler equations. As a model of a thermodynamic state, we take the Dieterici state equation. We investigate critical phenomena emerging along the flow of such gases. Namely, the solution of Euler equations in case of source is given and the domains in space where phase transition occurs are constructed.

Abstract—In this paper, novel spectral decompositions are obtained for the solutions of generalized Lyapunov equations, which are observed in the study of controllability and observability of the state vector in deterministic bilinear systems. The same equations are used in the stability analysis and stabilization of stochastic linear control systems. To calculate these spectral decompositions, an iterative algorithm is proposed that uses the residues of the resolvent of the dynamics matrix. This algorithm converges for any initial guess, for a nonsingular and stable dynamical system. The practical significance of the obtained results is that they allow one to characterize the contribution of individual eigen-components or their pairwise combinations to the asymptotic dynamics of the perturbation energy in deterministic bilinear and stochastic linear systems. In particular, the norm of the obtained eigen-components increases when frequencies of the corresponding oscillating modes approximate each other. Thus, the proposed decompositions provide a new fundamental approach for quantifying resonant modal interactions in a large and important class of weakly nonlinear systems.

The paper deals with the question of the solvability of inclusions F(x, σ) ∈ Q for mappings F close, in some metrics, to a given mapping ̂F.

Sufficient conditions for the local controllability of a control system of ordinary differential equations are presented. These conditions are meaningful in the case where the linear approximation of the system is not completely controllable. Second-order necessary conditions for optimality for the problem of optimal control are obtained as a corollary.