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.

This paper considers the problem of global asymptotic stability of a class of uncertain discrete-time systems under the influence of finite wordlength nonlinearities (quantization and/or overflow) and time-varying delays. The parameter uncertainties are assumed to be norm-bounded. Utilizing the concept of a Wirtinger-based inequality and a reciprocally convex method, two delay-dependent stability criteria are presented. The selection of the criteria depends on the type of the nonlinearities, that is, a combination of quantization and overflow or saturation overflow nonlinearities involved in the present systems. The approach presented in this paper yields less conservative results and reduces the computational burden as compared to previously reported criteria. Numerical examples are given to illustrate the effectiveness of the presented approach.

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The problem of global asymptotic stability of a class of uncertain discrete-time systems in the presence of saturation nonlinearities and interval-like time-varying delay in the state is considered. The uncertainties associated with the system parameters are assumed to be deterministic and normbounded. The objective of the paper is to propose stability criteria having considerably smaller numerical complexity. Two new delay-dependent stability criteria are derived by estimating the forward difference of the Lyapunov functional using the concept of reciprocal convexity and method of scale inequality, respectively. The presented criteria are compared with a previously reported criterion. A numerical example is provided to illustrate the effectiveness of the presented criteria.

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