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Nonlinear Dynamics

, Volume 59, Issue 4, pp 681–693 | Cite as

Feedback stabilization of a class of nonlinear second-order systems

  • Pawel Skruch
Original Paper

Abstract

The goal of this paper is to study stabilization techniques for a system described by nonlinear second-order differential equations. The problem is to determine the feedback control as a function of the state variables. It is shown that the following controllers can asymptotically stabilize the system: linear position feedback, linear velocity feedback and a group of nonlinear feedbacks. The stability of the corresponding closed-loop system is proved by imposing a suitable Lyapunov function and then using LaSalle’s invariance principle. The results of numerical computations are included to verify theoretical analysis and mathematical formulation. Some application examples from robotics, mechanics and electronics are presented.

Keywords

Nonlinear dynamical system Stability Lyapunov functions Nonlinear control Feedback stabilization 

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Department of AutomaticsAGH University of Science and TechnologyKrakowPoland

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