ABSTRACT

ToputarestrictiononthenoiseandtoconstructLyapunov-Krasovskii functionals we use the following auxiliary functions :

m L(u) = II In; (u + em + f) ,

;=0

<I>(u)

m N ( u) = II In; (u + em + f) , ( 1 )

;= 1

(2)

for u � 0 , where eo = 0 , e1 = 1 , em = eXp em_ 1 , lno (x) = x , In; (x) = In;_ l (ln x ) , i = I , 2 , . . . , m , x > 0 , f > O . These functions possess many useful properties . The appropriate references can be found in Ref [4]- [5] .