Stochastic eigenvalues for LTI systems with stochastic modes

The paper is concerned with a S-eigenvalue(stochastic-eigenvalue) concept in the linear time-invariant stochastic system where a stochastic mode in dynamics depends on stochastic uncertainties. The main contributions include the propositions of the new concept for S-eigenvalue, S-eigenvector (stochastic-eigenvector) and its probability density function in the complex plane. Numerical examples are presented to illustrate the proposed concepts.