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Title: New conditions for annular finite-time stability of linear systems
Authors: Amato, Francesco
De Tommasi, Gianmaria
Mele, Adriano 
Pironti, Alfredo
Issue Date: 2016
In this paper we investigate the annular finite-time stability (AFTS) problem for linear systems. A system is said to be annular finite-time stable if the norm of the system state remains within an upper and lower treshold for a given finite interval of time. Two necessary and sufficient conditions are provided for AFTS, the former requiring the solution of a differential Lyapunov equation (DLE), the latter involving an optimization feasibility problem constrained by differential linear matrix inequalities (DLMIs). We show that the DLE-based condition is more efficient from the computational point of view; however the DLMI-based condition is the starting point to investigate the design problem. To this regard a necessary and sufficient condition for the existence of a state feedback controller which renders the closed loop annular finite-time stable is provided. A numerical example illustrates the improvement of the proposed approach with respect to those existing literature.
ISBN: 9781509018376
DOI: 10.1109/CDC.2016.7799022
Appears in Collections:D1. Contributo in Atti di convegno

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