Journal
NONLINEAR DYNAMICS
Volume 59, Issue 4, Pages 681-693Publisher
SPRINGER
DOI: 10.1007/s11071-009-9570-4
Keywords
Nonlinear dynamical system; Stability; Lyapunov functions; Nonlinear control; Feedback stabilization
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Funding
- Ministry of Science and Higher Education in Poland [N N514 414034]
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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.
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