Improved stability results for uncertain discrete-time state-delayed systems in the presence of nonlinearities

In this paper, delay-dependent linear matrix inequality (LMI)-based stability conditions have been developed for uncertain discrete-time state-delayed systems, in which nonlinear effects in the form of limit cycles may arise due to the finite word length implementation of such systems. Two problems have been addressed in this paper. The first problem considers the discrete-time system to be under the combined influence of quantization and overflow nonlinearities and in the second problem, the system is under the influence of saturation nonlinearities. The criteria developed are based on utilizing both the delay partitioning method and reciprocally convex approach. It is demonstrated with the help of numerical examples that the presented criteria are able to yield less conservative results along with lower computational complexity than previously reported criteria.