Estimating the domain of attraction via union of continuous families of Lyapunov estimates.

*(English)*Zbl 1109.37012Summary: This paper proposes a new approach to estimate the domain of attraction of equilibrium points of polynomial systems. The idea consists of estimating the domain of attraction via the union of a continuous family of Lyapunov estimates rather than via one Lyapunov estimate only as done in existing methods. This family is obtained through a convex LMI optimization by deriving a stability condition which takes simultaneously into account all Lyapunov functions considered. Moreover, inner approximations to the union of this family via a set with simple shape are derived, too.

##### Keywords:

polynomial system; domain of attraction; Lyapunov function; parameter-dependent estimate; linear matrix inequality approach
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\textit{G. Chesi}, Syst. Control Lett. 56, No. 4, 326--333 (2007; Zbl 1109.37012)

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