This paper is devoted to stability analysis and synthesis of uncertain systems with time-varying delay. A newpar ame ter- dep en de nt L ya pun ovfunc tionana lyz ingapproach is proposed to reduce the conservativeness in delay-independent and delay-dependentstability analysis for the polytopic systems with time delay. Some new stability conditions are developed for the systems based on the Razumikhin stability theorem. A design method for general state feedback controllers is then proposed for the polytopic systems with time delay by the LMI optimization based approach. Numerical examples are used to demonstrate the effectiveness of the proposed design approach.