School of Mathematics and Physics, China University of Geosciences(Wuhan), 430074, Wuhan, China.
Education Department of Natural Science, Haikou College of Economics, 571127, Haikou, China.
ISA Trans. 2018 Jun;77:71-76. doi: 10.1016/j.isatra.2018.03.022. Epub 2018 Apr 10.
In this paper, we propose new sufficient criteria for input-to-state stability (ISS) of time-varying nonlinear discrete-time systems via indefinite difference Lyapunov functions. The proposed sufficient conditions for ISS of system are more relaxed than for ISS with respect to Lyapunov functions with negative definite difference. We prove system is ISS by two methods. The first way is to prove system is ISS by indefinite difference ISS Lyapunov functions. The second method is to prove system is ISS via introducing an auxiliary system and indefinite difference robust Lyapunov functions. The comparison of the sufficient conditions for ISS obtained via the two methods is discussed. The effectiveness of our results is illustrated by three numerical examples.
在本文中，我们通过不定差分 Lyapunov 函数，为时变非线性离散时间系统的输入到状态稳定性（ISS）提出了新的充分条件。与关于具有负定差分的 Lyapunov 函数的 ISS 相比，所提出的系统 ISS 的充分条件更为宽松。我们通过两种方法证明系统的 ISS。第一种方法是通过不定差分 ISS Lyapunov 函数证明系统的 ISS。第二种方法是通过引入辅助系统和不定差分鲁棒 Lyapunov 函数来证明系统的 ISS。讨论了通过这两种方法获得的 ISS 充分条件的比较。通过三个数值示例说明了我们的结果的有效性。
