scholarly journals Stability Criteria for Uncertain Discrete-Time Systems under the Influence of Saturation Nonlinearities and Time-Varying Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Siva Kumar Tadepalli ◽  
V. Krishna Rao Kandanvli ◽  
Haranath Kar
Keyword(s):  
Discrete Time ◽  
Time Varying ◽  
Stability Criteria ◽  
Time Varying Delay ◽  
Discrete Time Systems ◽  
Forward Difference ◽  
Delay Dependent ◽  
Time Systems ◽  
Delay Dependent Stability ◽  
Varying Delay

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.

scholarly journals Partitioning Technique for Relaxed Stability Criteria of Discrete-Time Systems with Interval Time-Varying Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Kuang-Yow Lian ◽  
Wen-Tsung Yang ◽  
Peter Liu
Keyword(s):  
Lyapunov Function ◽  
Discrete Time ◽  
Time Varying ◽  
Stability Criteria ◽  
Discrete Time System ◽  
Interval Time ◽  
Time Varying Delay ◽  
Discrete Time Systems ◽  
Time Systems ◽  
Varying Delay

We demonstrate an improved stability analysis based on a partition oriented technique for discrete-time systems with interval time-varying delay. The partition oriented technique introduces beneficial terms contributing to the negative definiteness of the Lyapunov function difference, meanwhile completely avoiding traditional inequality based approaches. In contrast, nonpartitioning oriented techniques do not put emphasis on further dividing the interval of the summation in the Lyapunov function. Herein, we demonstrate that the advantages of exploiting partitioning techniques manifest the relaxed stability criteria, as well as the flexibility to tune tradeoff between allowable timedelay range performance and computational load. Simulation carried out on a benchmark discrete-time system reveals the significant improvement in terms of maximum allowable upper bound in comparison.

Criteria for stability of uncertain discrete-time systems with time-varying delays and finite wordlength nonlinearities

2017 ◽  
Vol 40 (9) ◽  
pp. 2868-2880 ◽  
Author(s):  
Siva Kumar Tadepalli ◽  
V Krishna Rao Kandanvli ◽  
Abhilav Vishwakarma
Keyword(s):  
Discrete Time ◽  
Time Varying ◽  
Stability Criteria ◽  
Parameter Uncertainties ◽  
Computational Burden ◽  
Discrete Time Systems ◽  
Delay Dependent ◽  
Time Systems ◽  
Delay Dependent Stability ◽  
Selection Of

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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