A Note on the Global Asymptotic Stability
| Autor: | Mohammad Hejri |
|---|---|
| Rok vydání: | 2023 |
| DOI: | 10.21203/rs.3.rs-2555773/v1 |
| Popis: | This paper addresses the classical problem of global asymptotic stability analysis of nonlinear systems. The note followed in this paper looks at the necessity of an additional condition on the derivative of the Lyapunov function to achieve the global asymptotic stability missed in the original statement. The classical theorem and its proof, selected from some seminal references, are discussed. It is shown that the available proofs have been developed for a weaker version of the global asymptotic stability called as semi-global asymptotic stability by which state convergence is guaranteed within each compact set of entire space. The new additional condition extends the existing results to meet the main definition of global asymptotic stability in which the state convergence is guaranteed when the initial condition approaches infinity in the entire space. Numerical results illustrate the effectiveness of the proposed additional condition. |
| Databáze: | OpenAIRE |
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