Quasi-LPV Control Design for a Class of Underactuated Mechanical Systems

In this work, we present a quasi-linear parameter varying (quasi-LPV) control design approach for a class of underactuated mechanical systems in cascaded normal form. By incorporating linear system theory, robust control techniques, and linear matrix inequality (LMI) tools, a trajectorybased approach is employed to prove semi-global asymptotic stability of the closed-loop systems. The proposed controller can be applied to a wide class of mechanical systems with various degrees of underactuation. The simple structure of the controller facilitates its straightforward implementation for a variety of applications when compared to existing approaches. The controller is implemented for the translational oscillator with a rotational actuator (TORA) system and an underactuated quadrotor model to illustrate its broad applicability and effectiveness.