Synthesis of Lyapunov Functions using Formal Verification

Lukas Munser; Grigory Devadze; Stefan Streif

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arXiv · 2112.01835

Synthesis of Lyapunov Functions using Formal Verification

Lukas Munser·Grigory Devadze·Stefan Streif

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Abstract

Recent employments of SMT solvers within the Lyapunov function synthesis provided effective tools for automated construction of Lyapunov functions alongside with sound computer-assisted certificates. The main benefit of the suggested approach is the formal correctness and elimination of the numerical uncertainty. In the present work, we extend the SMT-based synthesis approach for wider classes of continuous and discrete-time systems. Additionally, we address constructions of Lyapunov functions for state-dependent switching systems. We illustrate our approach by means of various examples from the control systems literature.

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Lukas Munser, Grigory Devadze, Stefan Streif. 2021-12-03. Synthesis of Lyapunov Functions using Formal Verification. https://arxiv.org/abs/2112.01835

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