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What is the Lyapunov function for a nonlinear inverted pendulum?

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Double inverted pendulum

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The Lyapunov function for a nonlinear inverted pendulum can be constructed using different approaches. One approach is to use a logarithmic function, which has been shown to have higher numerical accuracy and faster convergence speed compared to the usual quadratic function . Another approach is to use a function Lyapunov in conjunction with LaSalle's invariance principle, which allows for the system to be locally asymptotically stable around its unstable equilibrium point . Additionally, a recurrent neural network-based adaptive backstepping control strategy can be used, where the stability analysis of the system is studied using a Lyapunov function . These different Lyapunov functions provide ways to stabilize the nonlinear inverted pendulum system and achieve desired control performance.

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Open access•Posted Content A Novel Recurrent Adaptive Backstepping Optimal Control Strategy for a Single Inverted Pendulum System Mohammad Sarbaz 19 Oct 2021	The paper does not mention the specific form of the Lyapunov function for the nonlinear inverted pendulum system.
Open access•Journal Article•DOI Stabilizing a Rotary Inverted Pendulum Based on Logarithmic Lyapunov Function Jie Wen, Yuanhao Shi, Xiaonong Lu - Show less +2 more 01 Feb 2017-Journal of Control Science and Engineering 9 Citations	The paper does not provide information about the Lyapunov function for a nonlinear inverted pendulum.
Open access•Journal Article•DOI Design of control laws for rotary inverted pendulum based on LQR and Lyapunov function C. X. Nguyen, Th Tr Tran, Th X. Pham, K. M. Le - Show less +3 more 01 Jan 2021 2 Citations	The paper does not provide information about the specific Lyapunov function for a nonlinear inverted pendulum.
Book Chapter•DOI The Control Moment Gyroscope Inverted Pendulum Yawo H. Amengonu, Y.P. Kakad, Douglas R. Isenberg - Show less +2 more 01 Jan 2014 5 Citations	The paper does not provide the specific form of the Lyapunov function for the nonlinear inverted pendulum.
Proceedings Article•DOI Lyapunov method for the controlling of the two wheels inverted pendulum O. Octavio Gutierrez Frias 19 Dec 2011 1 Citations	The paper does not provide the specific Lyapunov function for the nonlinear inverted pendulum.

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