## 1 Introduction
In this paper, we first apply a feedback linearization technique to well address above limitations with multi-performances including the almost disturbance rejection performance, the global stability, adjustable convergence rate and convergence radius. Recently, the feedback linearization technique has attracted many researches such as the autonomous arm [17], the swash mass helicopter [18], the wheeled inverted pendulum mobile robot [19], the bending soft pneumatic actuators [20], the cascaded power electronic transformer [21] and the grid-tied synchronerter [22]. Practical industrial systems are always corrupted by different types of unknown disturbances, and one important issue in robust controller design is to attenuate their influence on the output terminal as much as possible, since it is difficult to realize exact disturbance decoupling. When \"exact\" disturbance decoupling performance fails, it is natural to investigate the almost disturbance decoupling performance, which is to design a robust control that attenuates the influence of the unknown disturbance on the output terminal up to an arbitrary degree. Stricter definition of almost disturbance decoupling performance with simultaneous absolute-value sense, integration-value sense and input-to-state stable sense had been exploited in [23; 24; 25]. However, refs. [23; 24] have shown the fact that some specific control systems cannot achieve the almost disturbance decoupling performance subject to one sufficient condition that the discriminant functions should possess a \"complete\" condition such as the following control system: \(\dot{x}_{se,1}(t)=\tan^{-1}(x_{se,2})+\Omega_{n}(t)\), \(\dot{x}_{se,2}(t)=u_{ip}\), \(y_{op,1}=x_{se,1}\equiv u_{op,1}\), where \(\Omega_{n}\), \(u_{ip}\) and \(u_{op,1}\) denote the unknown disturbance, input and output, respectively. In contrast, this article applies the feedback linearization approach to address the almost disturbance decoupling performance for FLHBR systems. Finally, we perform a simulation by the traditional PID control in the simulation section to exploit the fact that the transient dynamics of the proposed feedback linearization approach such as the peak time, the rise time, the settling time and the maximum overshoot specifications is better than the traditional PID approach. The main contributions of the proposed approach in this study are summarized as follows:  
(1) The study first proposes the complete derivations of a mathematical model for highly nonlinear FLHBR systems. (2) This article first gives the formulas of exponential convergent rate and convergent radius for the FLHBR system. (3) The FLHBR system is addressed well by using the feedback linearization technique to take the place of traditional singular perturbation technique without the limitation that the discriminant function requires a complete condition [23,24]. (4) The exponential stability of FLHBR systems is guaranteed in this study without solving the troublesome Hamilton-Jacobi equation which is critical work for the traditional H-infinity approach [26]. (5) The article proposes a one-controller design of FLHBR systems to improve the severe shortcomings of traditional function approximators such as the fuzzy control approach and neural network control approach without relying on the experience of many experts accumulated in the past and complex interconnected neural network rules, respectively. (6) The proposed stability theorem of FLHBR systems in this article is global for whole state space and takes the place of the traditional Jacobian linearization technique that is only local for areas near the equilibrium point [27]. (7) This article designs a powerful human-machine interface of robust controller design for FLHBR systems using Python and dynamically shows the convergent trajectory of the system states.