%0 Journal Article
%T Stability Criteria for Uncertain Discrete-Time Systems under the Influence of Saturation Nonlinearities and Time-Varying Delay
%A Siva Kumar Tadepalli
%A V. Krishna Rao Kandanvli
%A Haranath Kar
%J ISRN Applied Mathematics
%D 2014
%R 10.1155/2014/861759
%X 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. 1. Introduction During the implementation of fixed-point state-space discrete-time systems using computer or digital hardware, one encounters finite wordlength nonlinearities such as quantization and overflow. Such nonlinearities may lead to instability in the designed system [1, 2]. Saturation overflow nonlinearity is one of the well-known nonlinear phenomena studied in the real world [3]. The stability analysis of discrete-time systems with state saturation is considered to be an important subject of system theoretic study [1¨C19]. Physical systems may suffer from parameter uncertainties that arise due to modeling errors, variations in system parameters, or some ignored factors. The existence of parameter uncertainties may result in instability of the designed system [20]. In the modeling of physical systems, time delays are often introduced due to finite capabilities of information processing and data transmission among various parts of the system [17, 20¨C22]. Such delays are another source of instability in discrete-time systems. The stability criteria for time delay systems are broadly classified into delay-independent and delay-dependent. In general, delay-dependent approach [15, 17, 18, 20, 22¨C37] leads to less conservative results as compared to delay-independent approach [16, 19, 20, 38]. The delay partitioning approach has been utilized in [30, 31] for the stability analysis of systems with interval-like time-varying delay. The stability analysis of discrete-time systems involving overflow nonlinearities, parameter uncertainties, and state delays is an important problem. Delay-independent stability criteria for a class of discrete-time state-delayed systems with saturation nonlinearities have been presented in [16, 19]. A delay-dependent approach for the stability analysis
%U http://www.hindawi.com/journals/isrn.applied.mathematics/2014/861759/