On damping of a nonlinear control system with delay

G.A.Kamenskii

Moscow State Aviation Institute

Volokolamskoe shosse, 4, Moscow 125252, Russia

The problem of damping of a control system with delay stated N.N.Krasovskii in [1]. He solved this problem for linear systems with delay.

There is considered here the nonlinear control system of the neutral type

(1)

with boundary value conditions

if (2) and

if (3)

with additional condition

, (4)

where .

If it is possible to solve equation (1) with regard to u

and

, (5)

then the damping of system (1) is equivalent to the problem of extremum of the nonlocal functional

(6)

with boundary conditions (2) and (3) for, if we put for , then it will be

for

In this paper there is proposed a method of solving the damping problem for more

general systems with delay of the neutral type that is based on theory of extrema of nonlocal functionals.

[1] N.N.Krasovskii. The theory of motion control. M.-Nauka, 1968. (In Russian.)