Operator-Based Segmental Control for Stabilization of Nonlinear Non-Minimum Phase Systems

This paper studies stabilization methods for non-minimum phase systems. Non-minimum phase systems are characterized by unstable zero dynamics and are represented by important systems such as rockets and aircraft. It is known that these systems cannot be exactly linearized or fully tracked, making control generally difficult. This paper proposes a method to stabilize non-minimum phase systems using operator theory, which is widely applicable in nonlinear control. First, a classification of minimum and non-minimum phase systems based on exact linearizability of nonlinear operators is defined. This classification allows for stabilization in minimum phase systems more concisely than previous operator theories. Next, a method to express non-minimum phase systems as the sum of two minimum phase systems is presented, enabling independent design for each system to achieve stabilization. Through this method, stabilization of non-minimum phase systems can be performed similarly to that of minimum phase systems. The effectiveness of the proposed method is verified through simulations using a wheeled inverted pendulum, confirming its validity.