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Necessary and Sufficient Dissipativity-Based Conditions for Feedback Stabilization

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posted on 05.01.2022, 21:23 authored by Diego de S. MadeiraDiego de S. Madeira
Using the notion of exponential QSR-dissipativity, this work presents necessary and sufficient conditions for exponential stabilizability of nonlinear systems by linear static output feedback (SOF). It is shown that, under mild assumptions, the exponential stabilization of the closed-loop system around the origin is equivalent to the exponential QSR-dissipativity of the plant. Furthermore, whereas strict QSR-dissipativity is only sufficient for SOF asymptotic stabilization, it is proved to be necessary and sufficient for full state feedback control. New necessary and sufficient conditions for SOF stabilizability of linear systems are presented as well, along with a linear and noniterative semidefinite strategy for controller design. Necessary linear matrix inequality (LMI) conditions for stabilization are also introduced. Some examples illustrate the usefulness of the proposed approach.

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Email Address of Submitting Author

dmadeira@dee.ufc.br

Submitting Author's Institution

Universidade Federal do Ceará

Submitting Author's Country

Brazil

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in IEEE Transactions on Automatic Control

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