Novel stability criteria for aperiodic sampled-data systems via a time-squared-dependent augmented functional

Zhen-Man Gao, Guo-Ping Liu, Yong He, Min Wu and Rukshan Navaratne

International Journal of Systems Science, 2021, vol. 52, issue 8, 1539-1550

Abstract: This paper is focusing on the stability analysis of aperiodic sampled-data systems. The augmented Lyapunov functional is powerful to produce a stability criterion with less conservatism owing to the well construction of coupled relationships among time-dependent states. In this paper, a novel augmented Lyapunov functional involving the time-squared-dependent augmented term is presented under the double-side looped-functional technique, which considers coupled relationships more fully than the current ones. Then, an improved negative definiteness lemma based on adjustable parameters is developed, resulting in a less conservative negative definite condition for the derivative of the Lyapunov functional. Finally, a stability criterion is derived based on the Lyapunov functional and the improved lemma, whose effectiveness is illustrated with four numerical examples and one practical example.

Date: 2021
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DOI: 10.1080/00207721.2020.1863502

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