Y. Ohta (Japan)
Attractive Region, Saturation, Linear Programming, Computational Geometry
We show how the combination of piecewise linear Lyapunov functions and star-shaped polytopic Lyapunov functions can be used to estimate attractive regions for linear systems with saturation. We first construct a piecewise linear Lyapunov function for a given system by using the linear programming method and the branch-and-bounding method, and compute the estimate of attractive region ac cording to the Lyapunov function. Then, we construct polytopes from obtained regions, and apply star-shaped polytopic Lyapunov function approach to improve the esti mate of attractive region. To demonstrate the usefulness of the proposed method we show some numerical examples.
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