Open AccessA Universal Formula for Asymptotic Stabilization with Bounded Controls
Author(s) -
Muhammad Nizam Kamarudin,
Abdul Rashid Husain,
Mohamad Noh Ahmad,
Zulkifli Mohamed
Publication year - 2015
Publication title -
international journal of electrical and computer engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.277
H-Index - 22
ISSN - 2088-8708
DOI - 10.11591/ijece.v5i1.pp111-118
Subject(s) - bounded function , control theory (sociology) , lyapunov function , exponential stability , benchmark (surveying) , nonlinear system , mathematics , stability (learning theory) , function (biology) , computer science , control (management) , mathematical analysis , physics , geodesy , quantum mechanics , artificial intelligence , machine learning , evolutionary biology , biology , geography
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.