Backstepping design for incremental stability of stochastic Hamiltonian systems with jumps. Jagtap, P. & Zamani, M. IEEE Transactions on Automatic Control, 63(1):255–261, January, 2018.
Backstepping design for incremental stability of stochastic Hamiltonian systems with jumps [link]Paper  doi  abstract   bibtex   
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.
@article{jagtap_backstepping_2018,
	title = {Backstepping design for incremental stability of stochastic {Hamiltonian} systems with jumps},
	volume = {63},
	copyright = {CC0 1.0 Universal Public Domain Dedication},
	issn = {0018-9286, 1558-2523},
	url = {http://ieeexplore.ieee.org/document/7961255/},
	doi = {10.1109/TAC.2017.2720592},
	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.},
	number = {1},
	urldate = {2018-11-01TZ},
	journal = {IEEE Transactions on Automatic Control},
	author = {Jagtap, Pushpak and Zamani, Majid},
	month = jan,
	year = {2018},
	pages = {255--261}
}

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