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Design of Saturating State-Feedback with Sign-Indefinite Quadratic Forms

Abstract : We propose a novel class of piecewise smooth Lyapunov functions leading to LMI-based stability/performance analysis and control design for linear systems with saturating inputs. We provide conditions for global properties, and also conditions for local properties and guaranteed estimates of the basin of attraction. The backbone of our result consists in using quadratic forms with constant matrices that are not necessarily sign definite, thereby providing additional degrees of freedom. Using generalized sector conditions involving the dead-zone nonlinearity and its derivative, we formulate convex optimization conditions to verify their positivity in the region of interest. Several numerical examples with connections to existing results, illustrate the potential behind our novel construction.
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https://hal.laas.fr/hal-03353776
Contributor : Isabelle Queinnec Connect in order to contact the contributor
Submitted on : Friday, September 24, 2021 - 12:43:40 PM
Last modification on : Tuesday, October 19, 2021 - 11:17:58 PM

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I. Queinnec, Sophie Tarbouriech, Giorgio Valmorbida, Luca Zaccarian. Design of Saturating State-Feedback with Sign-Indefinite Quadratic Forms. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, In press, ⟨10.1109/TAC.2021.3106878⟩. ⟨hal-03353776⟩

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