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

• Published in: Transactions of the Institute of Measurement and Control Vol. 40; no. 9; pp. 2868 - 2880
• Main Authors: Tadepalli, Siva Kumar, Kandanvli, V Krishna Rao, Vishwakarma, Abhilav
• Format: Journal Article
• Language: English
• Published: London, England SAGE Publications 01-06-2018; Sage Publications Ltd
• Subjects: Discrete time systems; Measurement; Parameter uncertainty; Stability criteria; Lyapunov method; time-varying delay; uncertain system; finite wordlength effect; Delay-dependent stability; linear matrix inequality
• ISSN: 0142-3312; 1477-0369
• DOI: 10.1177/0142331217709067

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.