On persistent excitation for linear systems with stochastic coefficients

A Wiener input process is shown to be persistently exciting (PE) for linear stochastic systems with time varying, convergent, random coefficients, provided the asymptotic noise controllability holds. The PE result is in the sense that the minimum eigenvalue of the integrated outer product of the state process is of O(t) (t being the upper time limit of the integral). Application examples are provided.