Abstract
Backstepping is one of the most popular frameworks for designing controllers for nonlinear systems. Its multiple advantages are well-known. It leads to a wide family of globally asymptotically stabilizing control laws, and it makes it possible to address robustness issues and solve adaptive control problems. This chapter begins with a review of classical backstepping for time-invariant systems. We then give several extensions that lead to timevarying strict Lyapunov functions and stabilizing feedbacks for time-varying systems. We first consider a general class of linear time-varying systems. Then we provide stronger results for linear systems in feedback form. Finally, we study nonlinear systems in feedback form and give conditions ensuring globally uniform stabilizability by bounded control laws.
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© 2009 Springer London
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(2009). Backstepping for Time-Varying Systems. In: Constructions of Strict Lyapunov Functions. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-1-84882-535-2_7
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DOI: https://doi.org/10.1007/978-1-84882-535-2_7
Publisher Name: Springer, London
Print ISBN: 978-1-84882-534-5
Online ISBN: 978-1-84882-535-2
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