On the Role of Coupled Damping and Gyroscopic Forces in the Stability and Performance of Mechanical Systems

Damping injection is a well-studied tool in nonlinear control theory to stabilize and shape the transient of mechanical systems. Interestingly, the injection of coupled damping yielding gyroscopic forces has received far less attention. This letter aims to fill this gap for gyroscopic forces that couple actuated and unactuated coordinates. First, we establish sufficient conditions for the stability of the closed loop. Then, we provide analytic results proving that injecting coupled damping may improve the closed-loop performance. We illustrate the results via the stabilization of three mechanical systems.