Delay-dependent Stability of Discrete-time Systems with Multiple Delays and Nonlinearities

A discrete-time system under finite wordlength implementation may demonstrate instability in its behavior. This instability is enhanced further in the presence of delays and parameter uncertainties. This paper, therefore, considers the problem of global asymptotic stability of a class of discrete-time systems in the presence of finite wordlength nonlinearities (combination of quantization and overflow nonlinearities), multiple delays and parameter uncertainties. Two linear matrix inequality (LMI) based delay-dependent stability criteria are proposed. The first criterion deals with the systems involving multiple delays of interval-like time-varying in nature and the second criterion is applicable to systems with multiple constant delays. The parametric uncertainties are time-varying and unknown but are assumed to be norm-bounded. The forward difference of the Lyapunov functional is treated using the reciprocally convex approach. Numerical examples highlighting the usefulness of the proposed criteria are provided.