Exponential stability of discrete time uncertain systems with time-varying delay (Q1916919)

This paper considers the robust stability of nonlinear uncertain delay systems of the form \[ x(k + 1) = Ax (k) + A_dx \bigl( k - i(k) \bigr) + \Delta A \bigl[ x(k) \bigr] + \Delta A_d \biggl[ x \bigl( k - i(k) \bigr) \biggr]. \] Using simple linear subestimates for the nonlinear terms, and a standard application of Lyapunov theory, three elementary theorems are proved on robust stability which require, essentially, \(|A |+ |A_d |+ |\Delta A |+ |\Delta A_d |< 1\).