Novel stability criteria for sampled-data systems with variable sampling periods

• Published in: IEEE/CAA journal of automatica sinica Vol. 7; no. 1; pp. 257 - 262
• Main Authors: Shao, Hanyong, Zhao, Jianrong, Zhang, Dan
• Format: Journal Article
• Language: English
• Published: Piscataway Chinese Association of Automation (CAA) 01-01-2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Asymptotic stability; Data systems; Delays; Sampled data systems; Sampling; Stability criteria; Symmetric matrices; Time dependence
• ISSN: 2329-9266; 2329-9274
• DOI: 10.1109/JAS.2017.7510376

This paper is concerned with a novel Lyapunovlike functional approach to the stability of sampled-data systems with variable sampling periods. The Lyapunov-like functional has four striking characters compared to usual ones. First, it is time-dependent. Second, it may be discontinuous. Third, not every term of it is required to be positive definite. Fourth, the Lyapunov functional includes not only the state and the sampled state but also the integral of the state. By using a recently reported inequality to estimate the derivative of this Lyapunov functional, a sampled-interval-dependent stability criterion with reduced conservatism is obtained. The stability criterion is further extended to sampled-data systems with polytopic uncertainties. Finally, three examples are given to illustrate the reduced conservatism of the stability criteria.