Mathematics in Science and Engineering, Volume 23Academic Press, 1966 - Engineering mathematics |
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absolute stability adjoint system admits a periodic almost-periodic solution bounded change of variables consider the system continuous corresponding cosē deduce defined denote differential equations dt dt dx(t dy dt eigenvalues follows Fourier transform fundamental matrix h₁ Halanay hence Hurwitzian inequality K₁ Lemma Let x(t lim sup h→0 lim x(t linear system linearly independent Lyapunov function monodromy matrix monotone-decreasing obtain periodic function periodic of period periodic solution perturbations Proof Proposition proved quadratic form respect sinē solution of system solutions of period sufficiently small suppose system admits t)da t₁ t₂ Taking into account Theorem trivial solution uniformly asymptotically stable unique periodic solution V. M. Popov V(to variational system vector verifies x(t₁ x(t₂ x₁ xo(t y(to αξ δο θε θο στ στ(ρ дх سلام