This note concerns delay-dependent robust stability criteria and a design method for stabilizing neutral systems with time-varying structured uncertainties. A new way of deriving such criteria is presented that combines the parameterized model transformation method with a method that takes the relationships between the terms in the Leibniz-Newton formula into account. The relationships are expressed as free weighting matrices obtained by solving linear matrix inequalities. Moreover, the stability criteria are also used to design a stabilizing state-feedbackcontr oller. Numerical examples illustrate the effectiveness of the method and the improvement over some existing methods.

This note concerns the problem of the robust stability of a linear system with a time-varying delay and polytopic-type uncertainties. In order to construct a parameter-dependent Lyapunov functional for the system, we first devised a new method of dealing with a time-delay system without uncertainties. In this method, the derivative terms of the state, which is in the derivative of the Lyapunov functional, are retained and some free weighting matrices are used to express the relationships among the system variables, and among the terms in the Leibniz-Newton formula. As a result, the Lyapunov matrices are not involved in any product terms of the system matrices in the derivative of the Lyapunov functional. This method is then easily extended to a system with polytopic-type uncertainties. Numerical examples demonstrate the validity of the proposed criteria.