Synthesis of Lyapunov Functions using Formal Verification

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 SMTbased 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.