Stability and response bounds of non-conservative linear systems

Abstract

This paper develops a stability theorem and response bounds for non-conservative systems of the form Mx+(D+G)x+(K+N)x=f(t), with hermitian positive-definite matrices M,D and K, and skew-hermitian matrices G and N. To this end, we first find a Lyapunov function by solving the Lyapunov matrix equation. Then, if a system satisfies the condition of the stability theorem, the associated Lyapunov function can be used to obtain response bounds for the norms as well as for the individual coordinates of the solution. Examples from rotor dynamics illustrate the results.