Stability Analysis and Response Bounds of Gyroscopic Systems

In this work, we develop a stability theorem for determining the stability or otherwise of a gyroscopic system. A Lyapunov function is obtained by solving the arising Lyapunov matrix equation. The Lyapunov function is then used to obtain response bounds for displacements and velocities both in the homogeneous and inhomogeneous cases. Examples are given to illustrate the efficacy of the results obtained.