Parameter-dependent control of an under-actuated mechanical system

Abstract

This papers applies parameter-dependent control to an under-actuated mechanical system; a two degree-of-freedom robot arm with only one actuator. Recent results on the use of a parameter-dependent Lyapunov function in the analysts and controller synthesis are investigated. The parameter-dependent model, where the parameters in this case are the two measured angles of the robot arms, captures the nonlinear behavior of the system in a prescribed operating range, unlike a set of linearized models. The application of parameter-dependent controllers to parameter-dependent systems is relevant in gain-scheduling. The synthesis procedure is formulated as a set of linear matrix inequality.