1. Lyapunov function and the basin of attraction for a single-joint muscle-skeletal model
- Author
-
Heiko Wagner and Peter Giesl
- Subjects
Lyapunov function ,Musculoskeletal Physiological Phenomena ,Lyapunov exponent ,Models, Biological ,Stability (probability) ,symbols.namesake ,Control theory ,Stability theory ,Elbow Joint ,Reflex ,Animals ,Humans ,Applied mathematics ,Lyapunov equation ,Lyapunov redesign ,Musculoskeletal System ,Control-Lyapunov function ,Mathematics ,Applied Mathematics ,Agricultural and Biological Sciences (miscellaneous) ,Attraction ,Biomechanical Phenomena ,Modeling and Simulation ,symbols ,Joints ,Muscle Contraction - Abstract
This paper provides an explicit Lyapunov function for a general single-joint muscle-skeletal model. Using this Lyapunov function one can determine analytically large subsets of the basin of attraction of an asymptotically stable equilibrium. Besides providing an analytical tool for the analysis of such a system we consider an elbow model and show that the theoretical predictions are in agreement with experimental results. Moreover, we can thus distinguish between regions where the self-stabilizing properties of the muscle-skeletal system guarantee stability and regions where nerval control and reflexes are necessary.
- Published
- 2006
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