Domain-of-attraction estimation for uncertain non-polynomial systems

• The problem of stability region analysis of uncertain non-polynomial systems is considered.
• A polynomial approximation method based on multivariate polynomial interpolation is proposed.
• From a reliable computational point of view, interpolation error is considered.
• The largest possible guaranteed subset of the DOA via a fixed Lyapunov function is computed.

In this paper, we consider the problem of computing estimates of the domain-of-attraction for non-polynomial systems. A polynomial approximation technique, based on multivariate polynomial interpolation and error analysis for remaining functions, is applied to compute an uncertain polynomial system, whose set of trajectories contains that of the original non-polynomial system. The efficiency of the presented method is illustrated by some numerical examples.