Stabilization and destabilization

This paper considers the stochastic stabilization and destabilization for uncertain nonlinear systems. Remarkably, the systems in question allow serious parameter unknowns (which don’t belong to any known constant set) and serious time-variations, and possess more general growth conditions than those in the related existing literature. The former feature makes the time-invariant scheme inapplicable, and a time-varying one is proposed, mainly to compensate the serious parameter unknowns, as well as serious time-variations. First, a time-varying stochastic noise is successfully constructed to super-exponentially stabilize the special but representative case without adverse serious time-variations. Then, for the general case and general decay rate, it suffices to find a fast enough time-varying gain for the stochastic noise. Moreover, by a time-varying method, the stochastic destabilization with general growth rate is also achieved for uncertain nonlinear systems