New delay-dependent stability criteria for discrete-time systems with an interval time-varying state delay

The asymptotical stability problem for a class of discrete-time systems with an interval time-varying state delay is investigated. A couple of stability criteria for this class of systems are obtained by constructing suitable Lyapunov functional and using linear matrix inequality techniques. On the one hand, it is mathematically proven that the first obtained stability criterion is less conservative and can be more simply computed than one given in [CCDC, 2010, pp. 2835-2839]. On the other hand, numerical examples indicate that the second obtained stability criterion may be less conservative or more suitable than exiting results.