Backstepping Design for Incremental Stability of Stochastic Hamiltonian Systems with Jumps

摘要

Incremental stability is a property of dynamical systems ensuring the uniformasymptotic stability of each trajectory rather than a fixed equilibrium pointor trajectory. Here, we introduce a notion of incremental stability forstochastic control systems and provide its description in terms of existence ofa notion of so-called incremental Lyapunov functions. Moreover, we provide abackstepping controller design scheme providing controllers along withcorresponding incremental Lyapunov functions rendering a class of stochasticcontrol systems, namely, stochastic Hamiltonian systems with jumps,incrementally stable. To illustrate the effectiveness of the proposed approach,we design a controller making a spring pendulum system in a noisy environmentincrementally stable.