Stability criteria for systems with interval time-varying delay

The cross-product terms in the derivative of Lyapunov-Krasovskii functional are disposed by using two integral-inequalities, and the state derivative term is reserved by employing Newton-Leibnitz formula and free-weighting matrix. First, stability criterion for nominal system is obtained, then applying S-procedure, stability criterion for linear fractional norm-bounded uncertainty system obtained. For system matrices and Lyapunov matrices in the stability condition of nominal system are separated, parameter-dependent Lyapunov-Krasovskii functional is used to deal with polytopic-type uncertainty system. Finally, numerical examples are given to demonstrate the effectiveness and are improvement of the proposed criteria.