Abstract:
The problems
$2p$-stability $(1 \le p < \infty)$ of systems of two linear Ito differential
equations with delay and impulse impacts on one component of solutions are
studied on the base of the theory of positively reversible matrices. Ideas
and methods developed by N. V. Azbelev and his followers to study the stability
problems of deterministic functional-differential equations are applied for this
purpose. Sufficient conditions for the $2p$-stability and exponential $2p$-stability
of systems of two linear Ito differential equations with delay and impulse impacts
on one component of solutions are given in terms of positive reversibility of the
matrices constructed from the parameters of the original systems. The validity of
these conditions is checked for specific equations. Sufficient conditions for
exponential moment stability of a system of two deterministic linear differential
equations with constant delay and coefficients with pulse influences on one
component of solutions are received in terms of parameters of this system.
It is shown that in this case from the general statements
it is possible to receive new results for the studied system.
Key words:Ito's
equations, stability of solutions, impulse impacts, positive
invertibility of a matrix.
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