Estimation of the domain of attraction for asymmetric saturated linear systems via Polyhedral Lyapunov Functions

This paper considers the problem of estimating the domain of attraction(DA) for continuous-time single-input asymmetric saturated linear systems. The stability analysis is implemented based on the polyhedral Lyapunov function rather than on the classical quadratic Lyapunov function. According to the saturation property, the saturated linear systems are regarded as switched linear systems, and a new sufficient condition for a polytope to be an estimation of the DA is derived. Moreover, a novel algorithm is proposed to compute the estimation of the DA. The effectiveness of the developed methods is illustrated with numerical examples..