High-Order Mean and Moment Exponential Stability Analysis Using Elimination and Duplication Matrices

This letter presents a necessary and sufficient condition for high-order moment stability of linear stochastic systems. Such a high-order stability notion is efficient as a metric of both stability and robustness to system randomness. The condition is established using two key matrices called the generalized elimination and duplication matrices, which efficiently represent high-order moment vectors. The high-order vector can be treated as the state variable of another linear deterministic system that involves the generalized matrices. The necessary and sufficient condition for the high-order moment stability is associated with the eigenvalues of the deterministic system. In addition, the high-order moment stability is equivalent to high-order mean stability if the order is even.