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arXiv · 1605.05486

Backstepping Design for Incremental Stability of Stochastic Hamiltonian Systems with Jumps

Pushpak Jagtap·Majid Zamani
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Abstract

Incremental stability is a property of dynamical systems ensuring the uniform asymptotic stability of each trajectory rather than a fixed equilibrium point or trajectory. Here, we introduce a notion of incremental stability for stochastic control systems and provide its description in terms of existence of a notion of so-called incremental Lyapunov functions. Moreover, we provide a backstepping controller design scheme providing controllers along with corresponding incremental Lyapunov functions rendering a class of stochastic control 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 environment incrementally stable.

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Pushpak Jagtap, Majid Zamani. 2016-05-18. Backstepping Design for Incremental Stability of Stochastic Hamiltonian Systems with Jumps. https://arxiv.org/abs/1605.05486

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