Logarithmic norm-based analysis of robust asymptotic stability of nonlinear dynamical systems. (English) Zbl 1456.34065
The article provides sufficient conditions for the robust (local and global) asymptotic stability of a semilinear differential equation in \(\mathbb{R}^n\). The conditions are given in terms of some integral estimates involving both the time-varying linear and nonlinear parts of the unperturbed equation and the time-varying nonlinear perturbation.
The contribution of the linear part is expressed in terms of the integral of the logarithmic norm of the time-varying matrix representing the linear dynamics. The construction of the logarithmic norm is recalled, and a discussion is provided on its dependence on the choice of a norm in \(\mathbb{R}^n\) (and its induced norm in the space of matrices). The combination of the different contributions is estimated using the variation of constants formula.
Several examples illustrate the effectiveness of the proposed sufficient conditions for robust asymptotic stability.
Reviewer: Mario Sigalotti (Paris)
MSC:
| 34D20 | Stability of solutions to ordinary differential equations |
| 34D10 | Perturbations of ordinary differential equations |
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