This paper addresses the asymptotic stabilization of a class of continuous-time nonlinear systems under a sampled-data control. The proposed approach is based on a quasi linear parameter varying (quasi-LPV) model for the nonlinear system and the use of a parameter dependent looped-functional to deal with the aperiodic sampling effects. Explicitly taking into account that the model parameters are functions of the state and therefore are bounded only in a given region of the state space, quasi-LMI conditions are proposed to compute a regional stabilizing nonlinear state feedback control law under aperiodic sampling. These conditions are then incorporated in convex optimization problems to compute the control law aiming at the maximization of an estimate of the region of attraction of the origin or the maximization of an upper bound on the intersampling time, with a guaranteed region of stability.

本文研究了一类连续时间非线性系统在采样数据控制下的渐近稳定。所提出的方法基于用于非线性系统的拟线性参数变化（quasi-LPV）模型，并使用依赖于参数的循环函数来处理非周期性采样效应。明确考虑到模型参数是状态的函数，因此仅在状态空间的给定区域内受限制，提出了拟LMI条件，以计算非周期性采样下的区域稳定非线性状态反馈控制律。