Almost Periodic Parameters for the Second Moment Stability of Linear Stochastic Systems

The technical note presents conditions to assure the uniform second moment stability for a class of linear time-varying stochastic systems. The system parameters are assumed to be almost periodic, a concept that is weaker than the periodic one. Under the existence of the long-run average cost associated with the stochastic system, we apply the almost periodicity to prove the desired stability result. An application illustrates the usefulness of the approach by implementing an almost periodic state-feedback strategy to control the velocity of a DC motor device.