ABSTRACT
Consider the following class of uncertain non-linear time-varying delay systems:
x A x A x B u f x
x
t
t
( ) ( )t ( ) ( )t ( )t( ) + ( ) ( )t + ( )t( )
( )t ( )t d τ
ϕ ∈[ ]− ⎧ ⎨⎪ ⎩⎪
(1)
where x n( )t ∈R and u m( )t ∈R denote the state and control input vectors, respectively. A, B and Ad are known real constant matrices with appropriate dimensions, ΔA, ΔB and ΔAd are real value unknown matrices representing time-varying parameter uncertainties. In this paper, the admissible parameter uncertainties are assumed to be of the following form:
MF[ ]Δ ΔA BΔ Ad ( )t [ ]E E E where M, E1 and E2 are real constant matrices and F i j( )t ∈R is an unknown time-varying matrix function satisfying F F I tT ( )t ( )t ≤ ∀, .
