Robust Stability and Stabilization for Uncertain Nonlinear System

The problem of delay-dependent robust stability and stabilization for a class of uncertain nonlinear systems with time-varying delay, is studied. The parameter uncertainty under consideration is norm bounded and possibly time- varying. The time delay considered here is assumed to be size- bounded but otherwise arbitrarily fast time-varying. Based on a special Lyapunov-Krasovakii functional, the delay-dependent stability condition is formulated in terms of linear matrix inequalities. The delay-independent result can be derived as a particular case for certain values of the tuning parameters. A numerical example is given to demonstrate the efficiency of the obtained results.