Delay-Dependent Stability Analysis of Delayed Discrete-Time Systems via State-Connecting-Based Zero-Value Equations

A simplified descriptor system approach is proposed for discrete-time systems with delays in terms of linear matrix inequalities. In comparison with the results obtained by combining the descriptor system approach with recently developed bounding technique, our approach can remove the redundant matrix variables while not reducing the conservatism. It is shown that the bounding technique is unnecessary in the derivation of our results. Via the proposed method, delay-dependent results on quadratic cost andH∞performance analysis are also presented.

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

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331217709067 ◽

2017 ◽

Vol 40 (9) ◽

pp. 2868-2880 ◽

Cited By ~ 9

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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Reciprocal convex approach to delay-dependent stability of uncertain discrete-time systems with time-varying delay

2012 American Control Conference (ACC) ◽

10.1109/acc.2012.6314609 ◽

2012 ◽

Cited By ~ 1

Author(s):

K. Ramakrishnan ◽

G. Ray

Keyword(s):

Discrete Time ◽

Time Varying ◽

Time Varying Delay ◽

Discrete Time Systems ◽

Delay Dependent ◽

Time Systems ◽

Delay Dependent Stability ◽

Varying Delay

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

ISRN Applied Mathematics ◽

10.1155/2014/861759 ◽

2014 ◽

Vol 2014 ◽

pp. 1-10 ◽

Cited By ~ 3

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.

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