New robust stability condition or uncertain discrete-time systems with time-varying delay

This paper is concerned with robust stability of uncertain discrete-time systems that have time-varying delay in state. Many researchers have been trying to consider such a problem and have given robust stability conditions via Linear Matrix Inequalities(LMIs). However, their conditions are rather conservative. To reduce conservativeness, we define a new Lyapunov function and use a Leibniz-Newton formula. Finally, we show that our conditions are less conservative than other results in some numerical examples.