where describes human operator’s ability to predict development of
information process,
is time estimation of informative perception, that depends on adaptive
abilities of human operator,
is value of reactive delay, determined with a training of human
operator. There is integrator for accumulating abilities. Median values of
parameters are
,
,
. Mathematical model of training human
operators has interval parameters, which vary not more than in 25 percents.
Consider a complex continuous-time dynamic system that has interval parameters only in a state matrix in the following form
;
;
, (8)
with state ,
external influence
, output
;
is state matrix of system with interval
parameters,
and
are input
and output matrices respectively:
;
,
.
Interval state matrix of system (8) consists of interval
scalar components
:
,
;
.
(9)
We will use two representations of interval state matrix. The first representation holds:
, (10)
with ,
, where
and
are corner realizations of interval
matrix
.
And second representation of interval matrix is decomposed with median and symmetric interval
components in the form
, (11)
where is median component of matrix
with the fixed scalar components
, determined by
, (12)
with elements in the following form
, (13)
and is symmetric interval matrix components of interval matrix
with symmetric corner realizations
and
satisfying equations
, (14)
. (15)
IV. FUNCTIONALS OF DEGENERATION OF COMPLEX SYSTEM WITH INTERVAL PARAMETERS
Obviously, functionals of degeneration of complex dynamic system, that is described by interval model, are interval values [1] and determined by the following form
, (16)
where is
interval criterion matrix of the
complex system such that
, (17)
with median component of interval criterion matrix
with fixed scalar components, symmetric interval
matrix component
of the interval criterion matrix
;
,
are maximum and
- interval singular
conditioning values of matrix
respectively.
Interval values of functionals of degeneration (16) are calculated with interval arithmetic [1].
Functionals of degeneration can be decomposed because of interval into two components:
, (18)
where is median component of interval functionals of degeneration
and
is symmetric interval component of interval functionals of
degeneration
. Its relative estimation can be
calculated by the following form
, (19)
and absolute estimation of interval functionals of degeneration such that
. (20)
Form interval criterion matrix of complex dynamic system (8) in
the form (17) for different model description external influence [7].
Interval criterion matrix of system (8) for a case of external multifrequency
harmonic influence
with a frequency
can be represented as
, (21)
where matrix satisfies to matrix equation of Sylvester [5, 6] with interval matrix
components in the following form
, (22)
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