Stochastic stability with S-eigenvalues in stochastic systems

This paper deals with an S-stability (stochastic-stability) using an S-eigenvalue (stochastic-eigenvalue) concept in the linear time-invariant stochastic system where a stochastic mode in dynamics depends on stochastic uncertainties. Our main contributions include the proposition of the S-stability concept for S-eigenvalue, S-eigenvector (stochastic-eigenvector) and its PDF (probability density function) in the complex plane. Numerical examples are presented to illustrate the proposed concepts.