A Semi-Algebraic Approach for the Computation of Lyapunov Functions

Z. She (Germany), B. Xia, and R. Xiao (PRC)

Keywords

Autonomous systems, Lyapunov functions, asymptotic sta bility, semialgebraic system, partialCAD.

Abstract

In this paper we deal with the problem of computing Lya punov functions for stability verification of differential sys tems. We concern on symbolic methods and start the dis cussion with a classical quantifier elimination model for computing Lyapunov functions in a given polynomial form, especially in quadratic forms. Then we propose a new semi-algebraic method by making advantage of the local property of the Lyapunov function as well as its deriva tive. This is done by first using real solution classifica tion to construct a semi-algebraic system and then solving this semi-algebraic system. Our semi-algebraic approach is more efficient in practice, especially for low-order systems. This efficiency will be evaluated empirically.

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