ИСТИНА

Let there be a smooth family of non - linear controlled systems of ordinary differential equations dx/dt=F(x,μ,u), x(M(R(m))),μ(L(R(k))),u(U(R(n))), F(C(∞))depending on the vector of controlling parameters u. Suppose that it is necessary to stabilize unstable limiting cycle x ⃰=(t,μ ⃰)of the period T, which is the solution of the family when u=0 and μ=μ ⃰. Let the system have a regular attractor when the parameters are of the same value u=0 a μ=μ ⃰. Then the stabilization of the cycle x ⃰=(t,μ ⃰) is carried out by means of the feedback with the delay being in the form of u(t)=K(x(t)-x(t-T)), where K - is the matrix of coefficients. Therewith the initial conditional x(0) is chosen in a sufficiently small vicinity of the cycle. Then the solution x(t) of the system dx/dt=F(x(t)),μ ⃰, K(x(t)-x(t-T))with the feedback with μ=μ ⃰can converge to the sought - for unstable cycle x= x ⃰.