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On output-based accelerated stabilization of a chain of integrators: Implicit Lyapunov-Krasovskii functional approach

Artem Nekhoroshikh 1, 2, 3 Denis Efimov 4 Andrey Polyakov 4 Wilfrid Perruquetti 2 Igor Furtat 5 Emilia Fridman 6
1 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
2 Centrale Lille
3 ITMO University [Russia]
4 VALSE - Finite-time control and estimation for distributed systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
5 IPME - Institute of Mechanical Engineering Problems [St. Petersburg]
6 Department of Electrical Engineering
Abstract : The problem of output accelerated stabilization of a chain of integrators is considered. Proposed control law nonlinearly depends on the output and its delayed values, and it does not use an observer to estimate the unmeasured components of the state. It is proven that such a nonlinear delayed control law ensures practical output stabilization with rates of convergence faster than exponential. The effective way of computation of feedback gains is given. It is shown that closed-loop system stability does not depend on the value of artificial delay, but the maximum value of delay determines the width of stability zone. The efficiency of the proposed control is demonstrated in simulations.
Keywords : Implicit Lyapunov-Krasovskii Functional (ILKF) Nonlinear control Delay-dependent output feedback Linear Matrix Inequalities (LMIs) Practical stability
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Submitted on : Wednesday, May 27, 2020 - 3:37:30 PM
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Artem Nekhoroshikh, Denis Efimov, Andrey Polyakov, Wilfrid Perruquetti, Igor Furtat, et al.. On output-based accelerated stabilization of a chain of integrators: Implicit Lyapunov-Krasovskii functional approach. IFAC 2020 - 21rst IFAC World Congress, Jul 2020, Berlin, Germany. ⟨hal-02634521⟩

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