Stochastic eigenstructure assignment with S-stability

This paper is concerned with an S-eigenvalue (stochastic-eigenvalue) concept in linear time-invariant stochastic systems, where a stochastic mode in dynamics depends on both the external disturbance and the inner-parameter variations. Our main contributions include the proposition of the new concept of the S-eigenvalue, S-eigenstructure (stochastic-eigenstructure) assignment, and S-stability (stochastic-stability) for LTI stochastic systems with stochastic modes. These results explicitly characterize how S-eigenvalues, S-eigenvectors and their PDFs (probability density functions) in the complex plane may impose S-stability on S-eigenstructure assignment.