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Control and Estimation in Finite-Time and in Fixed-Time via Implicit Lyapunov Functions

Abstract : This work presents new results on analysis and synthesis of finite-time and fixed-time stable systems, a type of dynamical systems where exact convergence to an equilibrium point is guaranteed in a finite amount of time. In the case of fixed-time stable systems, this is moreover achieved with an upper bound on the settling-time that does not depend on the system’s initial condition. Chapters 2 and 3 focus on theoretical contributions; the former presents necessary and sufficient conditions for fixed-time stability of continuous autonomous systems whereas the latter introduces a framework that gathers ISS Lyapunov functions, finite-time and fixed-time stability analysis and the implicit Lyapunov function approach in order to study and determine the robustness of this type of systems. Chapters 4 and 5 deal with more practical aspects, more precisely, the synthesis of finite-time and fixed-time controllers and observers. In Chapter 4, finite-time and fixed-time convergent observers are designed for linear MIMO systems using the implicit approach. In Chapter 5, homogeneity properties and the implicit approach are used to design a fixed-time output controller for the chain of integrators. The results obtained were verified by numerical simulations and Chapter 4 includes performance tests on a rotary pendulum.
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https://hal.inria.fr/tel-02071668
Contributor : Francisco Lopez Ramirez <>
Submitted on : Monday, March 18, 2019 - 4:18:31 PM
Last modification on : Tuesday, September 29, 2020 - 12:24:07 PM
Long-term archiving on: : Wednesday, June 19, 2019 - 6:24:02 PM

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  • HAL Id : tel-02071668, version 1

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Francisco Lopez-Ramirez. Control and Estimation in Finite-Time and in Fixed-Time via Implicit Lyapunov Functions. Physics [physics]. Université de Lille, 2019. English. ⟨tel-02071668⟩

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