Abstract
A class of homogeneous polynomial functions is used to estimate the attractive stability region for an impulsive switched linear system with saturated control input. Under the arbitrary switching rule and the dwell time switching rule, local stabilization conditions are obtained in terms of linear matrix inequalities. The corresponding optimization problems are formulated to obtain a larger attractive stability region. Using the simple ellipsoid method to estimate the attractive stability region produces very conservative results, because the attractive stability region is normally irregular. To solve this problem, a polyhedron constructed using a level set of the homogeneous parameter-dependent quadratic Lyapunov function is used to estimate the attractive stability region. The polyhedron is closer to the attractive stability region than the simple ellipsoid. Finally, numerical examples are given to demonstrate the effectiveness of the proposed method.
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