LMI-Based Composite Nonlinear Feedback Tracker for Uncertain Nonlinear Systems With Time Delay and Input Saturation

Abstract

This study proposes a composite nonlinear feedback approach for the robust tracking control problem of uncertain nonlinear systems with input saturation, Lipschitz nonlinear functions, multivariable time-delays, and disturbances. The composite nonlinear feedback technique includes two components: a linear feedback portion constructed in such a way that it changes the damping ratio so as to speed up the system’s response. A nonlinear feedback controller is designed to further increment the damping ratio in a way that it ensures the tracking whilst reducing the overshoot created by the linear portion. By creating a suitable Lyapunov functional and by using the linear matrix inequality (LMI) approach, the LMI conditions are determined to guarantee system stability and obtain the required design parameters. The performance of the proposed approach is assessed using a simulation study of a two-dimensional system along with a Chua’s circuit system. The advantages of the proposed approach are its less-restrictive assumptions, improved transient performance, and steady-state precision.

Keywords

• Composite nonlinear feedback
• input saturation
• linear matrix inequality
• robust tracking
• time delay