Acceleration of finite-time stable homogeneous systems

Yotam Dvir 1 Arie Levant 1 Denis Efimov 2 Andrey Polyakov 2 Wilfrid Perruquetti 2
2 NON-A - Non-Asymptotic estimation for online systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : Stabilization rates of power-integrator chains are easily regulated. It provides a framework for acceleration of uncertain multi-input multi-output (MIMO) dynamic systems of known relative degrees (RDs). The desired rate of the output stabilization (sliding-mode (SM) control) is ensured for an uncertain system, if its RD is known, and a rough approximation of the high-frequency gain matrix is available. The uniformly bounded convergence time (fixed-time stability) is obtained as a particular case. The control can be kept continuous everywhere accept the SM set, if the partial RDs are equal. Similarly uncertain smooth systems of complete MIMO RDs (i.e. lacking zero dynamics) are stabilized by continuous control at their equilibria in finite time and also accelerated. Output-feedback controllers are constructed. Computer simulation demonstrates the efficiency of the proposed approach.
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Yotam Dvir, Arie Levant, Denis Efimov, Andrey Polyakov, Wilfrid Perruquetti. Acceleration of finite-time stable homogeneous systems. International Journal of Robust and Nonlinear Control, Wiley, 2017, 00, pp.1 - 23. ⟨10.1002/rnc⟩. ⟨hal-01611961⟩

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