Input-Output Feedback Linearization: Case Study on 2—Contractive Zero Dynamics

Zero dynamics are essential to the design and analysis of input-output feedback linearization control, particularly in nonlinear systems. This study revisits an input-output feedback linearization problem through an illustrative example where the zero dynamics admits multiple equilibrium points. The effect of such zero dynamics on system performance and control input has also been investigated. Conventional tools such as 1-contraction and Lyapunov theory are not directly applicable to the analysis of zero dynamics with multiple equilibria. Therefore, the theory of 2-contraction is employed to perform the analysis effectively. The impact of such zero dynamics on the external control input, tasked with regulating the system's output is also analyzed. Extensive numerical simulations are conducted to validate and exemplify the theoretical results.