Learning Lyapunov Operators for Nonlinear Systems
Constructing Lyapunov functions for nonlinear dynamical systems is a central problem in stability analysis, yet remains challenging. Lyapunov functions are commonly characterized as solutions to first-order partial differential equations (PDEs), but these solutions are typically obtained for single systems, limiting their reuse across systems. In this paper, we study the Lyapunov solution operator that maps a vector field to the corresponding Lyapunov function defined by a dissipation-based Lyapunov PDE. We establish that, on compact subsets of the domain of attraction and under exponential stability assumptions, this operator is well-defined, unique, and continuous with respect to pertur...
| Authors | Amartya Mukherjee, Maxwell Fitzsimmons, David C. Del Rey Fernández et al. |
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| Primary category | math.AP |
| Published | 16 September 2026 |
| Last updated at source | 16 September 2026 |
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