2010/02/10 by Bahman Gharesifard, Gharesifard, Bahman
Engineering · Mathematics · #70H14 #70Q05 #93B27 #93C10 #93D15 #Control and Stability of Dynamical Systems #Dynamics and Control of Mechanical Systems #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations #math.OC #msc:70H14 #msc:70Q05 #msc:93B27 #msc:93C10 #msc:93D15
paper · pdf · doi:10.48550/arxiv.1002.2135
arxiv created 2010/02/10 · openalex publication_date 2010/02/10 · arxiv updated 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A geometric formulation for stabilization of systems with one degree of underactuation which fully solves the energy shaping problem for these system is given. The results show that any linearly controllable simple mechanical system with one degree of underactuation is stabilizable by energy shaping, possibly via a closed-loop metric which is not necessarily positive-definite. An example of a system with one degree of underactuation is provided for which the stabilization by energy shaping method is not achievable using a positive-definite closed-loop metric.