Delay-dependent robust stabilization for uncertain linear system

The problem of delay-dependent robust stabilization for a class of uncertain linear systems with time-varying delay is investigated. 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 state-feedback control law is also given such that the resultant closed-loop system is stable for admissible uncertainties. Two numerical examples are given to demonstrate the efficiency of the obtained results.