Synthesis of Lyapunov Functions using Formal Verification

TL;DR

This paper extends SMT-based methods for synthesizing Lyapunov functions, enabling formal, sound, and automated stability analysis for broader classes of systems, including switching systems.

Contribution

It introduces an extended SMT-based approach for Lyapunov function synthesis applicable to continuous, discrete, and switching systems, enhancing automation and correctness.

Findings

Successfully applied to various control systems examples

Extended to state-dependent switching systems

Ensures formal correctness and eliminates numerical uncertainty

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.