Regional stabilization of nonlinear sampled-data control systems: A quasi-LPV approach

• Published in: European journal of control Vol. 59; pp. 301 - 312
• Main Authors: Palmeira, Alessandra H.K., Gomes da Silva, João M., Flores, Jeferson V.
• Format: Journal Article
• Language: English
• Published: Philadelphia Elsevier Ltd 01.05.2021; Elsevier Limited
• Subjects: Approximation; Behavior; Closed loop systems; Computational geometry; Control systems; Control theory; Convexity; Feedback control; Linear matrix inequalities (LMI); Mathematical models; Maximization; Nonlinear control; Nonlinear systems; Optimization; Parameters; Quasi-LPV control; Regional stability; Sampled-data control; Sampling; Stabilization; State feedback; Upper bounds; Validity; Sampled-data control; Linear matrix inequalities (LMI); Quasi-LPV control; Nonlinear systems; Regional stability
• ISSN: 0947-3580; 1435-5671
• DOI: 10.1016/j.ejcon.2020.11.001

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.