H∞ Robust LMI-Based Nonlinear State Feedback Controller of Uncertain Nonlinear Systems with External Disturbances

Abstract

In this paper, we propose a nonlinear state feedback controller based on linear matrix inequality (LMI) for a class of nonlinear systems with parametric uncertainties and external disturbances. The primary goals of the proposed controller are to guarantee system stability and performance in the presence of system uncertainties and time-dependent disturbances. To meet the specified objectives, the LMI form is calculated as a hierarchical control structure. Using the Lyapunov stability function, the asymptotic stability of the nominal system obtained from the nonlinear state feedback is proven, and the LMI condition is attained. After applying the nonlinear state feedback controller, asymptotic stability conditions for the nominal system are constructed using the Lyapunov function, and the nonlinear state-feedback control mechanism is determined accordingly. Considering the external disturbance as input, the terms of the state matrices are substituted in the obtained LMI, and the LMI condition for a nominal system is achieved in the presence of disturbances. The asymptotic stability condition of the uncertain system in the presence of external disturbances is determined by adding uncertainties to the system. The proposed approach yields a simple control mechanism representing an independent of system order. The performance of the proposed approach was assessed using a simulation study of a ball and beam system.

Path Tracking Control Based on T-S Fuzzy Model for Autonomous Vehicles with Yaw Angle and Heading Angle

“…The system state is realized to attain equilibrium more quickly in a finite amount of time by using robust control techniques, and linear matrix inequality (LMI) determines the control parameters. A state feedback controller is suggested in [19] to maintain system performance and stability in the face of time-varying disturbances and system uncertainty. A method of learning-based control for autonomous cars is presented in this research.…”

Evaluation of Ride Performance of Active Inerter-Based Vehicle Suspension System with Parameter Uncertainties and Input Constraint via Robust H∞ Control

“…To find a compromise between the conflicting performances of the vehicle suspension system, many approaches have been proposed based on various control techniques, such as sliding mode control [15,16], fuzzy logic and neural network control [1,17], model predictive control [18], adaptive control [15,17], H ∞ control [2,[19][20][21], etc. In particular, the application of robust H ∞ control of the active vehicle suspension system in the context of robustness and damping of road disturbances has been intensively investigated.…”

“…In [2], a delay-dependent memory state-feedback H ∞ controller for active quarter-car suspension system with input time-delay in the presence of external disturbance were investigated. In [21], for a class of nonlinear systems under parametric uncertainties and external disturbances, a nonlinear state feedback controller based on linear matrix inequality was presented. Considering all these works, we intend to investigate the active inerterbased suspension system for a quarter-car model by considering all factors, including external disturbance, parametric uncertainty, and input constraint.…”