LMI-based LSVF control of a class of nonlinear systems with parametric uncertainty: an application to an inverted pendulum system

ABSTRACT

This work centres around the stabilisation of a nonlinear system containing parametric uncertainty using a new Control Lyapunov Function (using Lie derivatives) which comes up with a linear matrix inequality-based design. The paper has three major contributions. The first one is an extension of a theorem proposed to find the convex-concave bounds of nonlinear function towards robustness. With some restrictions in the structure of the uncertainty, the theory developed here may be applied to find out the bounds of any nonlinear function with uncertainty. The next one is the main contribution of this paper in which the form of the control law obtained is linear and has several advantages from a practical point of view over almost all other nonlinear control techniques. The third one is the expansion of the proposed control scheme towards underactuated systems. To show the effectiveness of the proposed theory the controller design is attempted for both the traditional cart inverted pendulum and the more complex mobile wheeled inverted pendulum model.

KEYWORDS:

• Nonlinear systems
• robust control
• linear matrix inequalities (LMI)
• linear state variable feedback (LSVF) control
• inverted pendulum system

Acknowledgments

This work is supported by Technical Education Quality Improvement Programme (TEQIP-II) of Indian Institute of Engineering Science and Technology, Shibpur. The authors remain grateful to the anonymous reviewers for improving the quality of the paper.

Additional information

Funding

Technical Education Quality Improvement Programme (TEQIP-II) of Indian Institute of Engineering Science and Technology, Shibpur.