Stability Analysis of Nonlinear Time-Varying Systems by Lyapunov Functions with Indefinite Derivatives

By Bin Zhou. 2015

108 citations recorded by the source corpus.

This paper is concerned with stability analysis of nonlinear time-varying systems by using Lyapunov function based approach. The classical Lyapunov stability theorems are generalized in the sense that the time-derivative of the Lyapunov functions are allowed to be indefinite. The stability analysis is accomplished with the help of the scalar stable functions introduced in our previous study. Both asymptotic stability and input-to-state stability are considered. Particularly, for asymptotic stability, several concepts such as uniform and non-uniform asymptotic stability, and uniform and non-uniform exponential stability are studied. The effectiveness of the proposed theorems is illustrated by several numerical examples.

Subfields: Applied Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/f18fc5c9dc1933dde17377d8da0c12601416aff1

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In Applied Mathematics

1. Peng Shi
2. Peng Shi
3. Yang Tang
4. Xiaotai Wu
5. Wenbing Zhang

In Control and Systems Engineering

1. Peng Shi
2. Peng Shi
3. Yang Tang
4. Xiaotai Wu
5. Wenbing Zhang
6. Shaocheng Tong
7. Fanbiao Li
8. Yong-ming Li

Citations in the corpus

• Input‐to‐state stability of nonlinear stochastic time‐varying systems with impulsive effects (2017, methodology): “In addition, stochastic disturbances and impulses were overlooked in [35, 36].”