Piecewise Linear Estimate of Attractive Regions for Linear Systems with Saturating Control

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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