Improved stability criteria for linear time-varying systems on time scales

ABSTRACT

In this paper, asymptotic stability problems of linear time-varying (LTV) systems on time scales are considered based on a less conservative Lyapunov inequality, whose right side is not required to be necessarily negative. It is shown that the Lyapunov inequality covers not only the corresponding trivial (continuous and discrete) ones but also nontrivial ones. Based on this inequality, some necessary and sufficient conditions for asymptotic stability, exponential stability, uniformly exponential stability of LTV systems on time scales are obtained. An example about nontrivial systems is given for illustrating the effectiveness of the proposed results.

KEYWORDS:

• Linear time-varying systems
• asymptotic stability
• Lyapunov inequality
• time scale

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the National Natural Science Foundations of China (61573215) and the Natural Science Fund for Distinguished Young Scholars of Shandong Province under grant JQ201613.