Stabilization and destabilization of nonlinear systems via aperiodically intermittent stochastic noises: Average techniques and scalar functions

In this paper, almost sure exponential stabilization and destabilization criteria for nonlinear systems are obtained via aperiodically intermittent stochastic noises based on average techniques and piecewise continuous scalar functions. Compared with existing results on almost sure exponential stability of stochastic systems, the requirement on the upper bound of the diffusion operator of a Lyapunov function is released. The upper bound is allowed to be a scalar function and even be unbounded. Simultaneously, by means of putting forward new concepts “average noise control rate” and “average noise control period,” assumptions on infimum of control time and supremum of rest time in the previous references about aperiodically intermittent control can be removed without implementing in the upper limit of the uncontrolled rate, which reduces the conservativeness of stabilization criteria resulting from non-uniform distribution of control time and rest time. In addition, the main results are applied to coupled and uncoupled nonlinear spring–mass–damper oscillator systems, respectively, and corresponding numerical simulations are carried out to demonstrate the validity of the theoretical analysis.