Method of forbidden regions in the dynamic system matrices root clustering problem

Abstract

New criteria for root-clustering of the dynamic system matrices in multiply connected regions were presented. A concept of the forbidden region was introduced, and a generalization of the Lyapunov-Jury theorem onto the multiply connected regions was proposed. The necessary and sufficient conditions for root-clustering outside the forbidden region were established as a sequence of matrix inequalities. Construction of the conditions for root-clustering outside the frequency bands and robust root-clustering in multiply connected region was illustrated by way of examples.

On the equation of fourth order with quadratic nonlinearity

“…For the construction of solutions of nonlinear differential equations in partial derivatives [6][7][8][9][10][11][12] is used different analytical and numerical methods: the perturbation methods, the small parameter method, the separation of variables method, the linearization method, the averaging method, the method of the stretched coordinates, the method of composite expansions, grid methods -the method of finite differences and the finite element method [13][14][15][16][17][18][19].…”

Mathematical modeling vibration protection system for the motor of the boat

“…For the calculation of nonlinear dynamic systems apply different methods [14][15][16][17][18][19]. Is applied known methods: the method of Van der Pol, harmonic balance method, averaging method, the method of small parameter, the method of Krylov-Bogolyubov, method of polynomial transformations, the Poincare perturbation method [20][21][22][23][24][25].…”