A Universal Formula for Asymptotic Stabilization with Bounded Controls

Motivated by Artstein and Sontag universal formula, this brief paper presents an explicit proof of the universal formula for asymptotic stabilization and asymptotic disturbance rejection of a nonlinear system with mismatched uncertainties and time varying disturbances. We prove the stability via Lya...

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Published inInternational journal of electrical and computer engineering (Malacca, Malacca) Vol. 5; no. 1; pp. 111 - 118
Main Authors Kamarudin, Muhammad Nizam, Husain, Abdul Rashid, Ahmad, Mohamad Noh, Mohamed, Zaharuddin
Format Journal Article
LanguageEnglish
Published Yogyakarta IAES Institute of Advanced Engineering and Science 01.02.2015
Subjects
Asymptotic properties
Control equipment
Disturbances
Dynamical systems
Mathematical models
Nonlinear dynamics
Stability
Stabilization
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Summary:Motivated by Artstein and Sontag universal formula, this brief paper presents an explicit proof of the universal formula for asymptotic stabilization and asymptotic disturbance rejection of a nonlinear system with mismatched uncertainties and time varying disturbances. We prove the stability via Lyapunov stability criteria. We also prove that the control law satisfies small control property such that the magnitude of the control signal can be bounded without the catastropic effect to the closed loop stability. For clarity, we benchmark the proposed approach with other method namely a Lyapunov redesign with nonlinear damping function. We give a numerical example to verify the results.
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ISSN:2088-8708
2088-8708
DOI:10.11591/ijece.v5i1.pp111-118