Stability of second-order multidimensional linear time-varying systems

This paper presents stability issues of second-order multidimensional linear time-varying systems. The second-order form is a result of modeling a class of dynamical systems directly using their physical parameters (e.g., inertia matrix). Three sufficient conditions for stability and two for instability were derived. Lyapunov's second method is first used to derive a sufficient stable condition which gives a range of variation for each parameter matrix. A new analysis method is used to derive a stable and an unstable condition. This method gives conditions on the integral of certain quantities. In this way, unlike conditions imposed by a typical Lyapunov analysis, instantaneous values of these quantities do not directly affect the proof of stability.