Abstract
SummaryThis paper addresses the estimation of the domain of attraction for a class of hybrid nonlinear systems where the state space is partitioned into several regions. Each region is described by polynomial inequalities, and the union of all the regions is a complete cover of the state space. The system dynamics are defined on each region independently from the others by polynomial functions. First, the problem of computing the largest sublevel set of a Lyapunov function included in the domain of attraction is considered. An approach is proposed for addressing this problem based on linear matrix inequalities, which provides a lower bound of the sought estimate by establishing negativity of the Lyapunov function derivative on each region. Second, a sufficient and necessary condition is provided for establishing optimality of the found lower bound, which requires to solve linear algebra operations in typical cases. Third, the problem of looking for Lyapunov functions that maximize the estimate of the domain of attraction is considered, describing several strategies where the proposed approach can be readily adopted. Copyright © 2014 John Wiley & Sons, Ltd.
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