Time Varying Delay Systems

The development of the hardware systems has incurred various types of delays such as processing and transmission delays. Such delay may be due to the effect of tolerances of electronic components which were used while developing the system. Such time delay parameters must be implemented in the transfer function of the system so as to identify the correct cause of dynamic behavior of the system which in turn affects the stability of the system. For the development of the accurate system it is required to consider the condition for the global robust asymptotic stability. Criteria for verifying robust stability are formulated as feasibility problems over a set of frequency dependent linear matrix inequalities. The criteria can be equivalently formulated as SemiDefinite Programs (SDP) using Kalman-Yakubovich-Popov lemma. Therefore, checking robust stability can be performed in a computationally efficient fashion. The Lyapunov-Krasovskii approach is definitely the most popular method to address this issue and many results have proposed new functionals and enhanced techniques for deriving less conservative stability conditions. The paper surveys the techniques used for developing the stable system from the various literatures published recently and draws the result that which method is best to develop a reliable and stable systems. KeywordsSemi-Definite Programs (SDP), Stability, Time Varying System, Integral Quadratic