A T–S Fuzzy Approach to the Local Stabilization of Nonlinear Discrete-Time Systems Subject to Energy-Bounded Disturbances

• Published in: Journal of control, automation & electrical systems Vol. 26; no. 3; pp. 191 - 200
• Main Authors: Klug, Michael, Castelan, Eugênio B., Coutinho, Daniel
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.06.2015
• Subjects: Control; Control and Systems Theory; Electrical Engineering; Engineering; Mechatronics; Robotics; Robotics and Automation; Energy-bounded disturbances; Nonlinear T–S models; Local stability; gain
• ISSN: 2195-3880; 2195-3899
• DOI: 10.1007/s40313-015-0172-8

This paper addresses the local stabilization problem of nonlinear discrete-time systems subject to energy-bounded disturbances by means of T–S fuzzy models. A fuzzy state feedback controller is designed such that the input-to-state stability in the ℓ 2 sense of the original nonlinear system is guaranteed in a bounded region of the state space. Such a region is related to the exactness of the T–S model and describes the domain around the origin where the convexity property remains valid. In addition, an estimate of the closed-loop reachable set is provided for a given class of ℓ 2 disturbances. Three (convex) optimization problems are proposed to either minimize the estimate of the reachable set, improve the disturbance tolerance or minimize the ℓ 2 -gain from the disturbance input to the regulated output. Numerical examples are considered to illustrate the approach demonstrating the effectiveness of the proposed technique for the control synthesis of nonlinear discrete-time systems.