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

摘要

We show how the combination of piecewise linear Lyapunovrnfunctions and star-shaped polytopic Lyapunov functionsrncan be used to estimate attractive regions for linearrnsystems with saturation. We first construct a piecewisernlinear Lyapunov function for a given system by using thernlinear programming method and the branch-and-boundingrnmethod, and compute the estimate of attractive region accordingrnto the Lyapunov function. Then, we constructrnpolytopes from obtained regions, and apply star-shapedrnpolytopic Lyapunov function approach to improve the estimaternof attractive region. To demonstrate the usefulness ofrnthe proposed method we show some numerical examples.