Stability Analysis of Cyber-Physical Systems via Dynamic Feedback Linearization and Linear Matrix Inequalities

Nonlinear control is a challenging aspect in modeling and controlling complex systems, specifically Cyber-Physical Systems (CPSs), where the system dynamics are inherently nonlinear. Robotics and autonomous vehicle applications mandate the need for stability and robustness guarantees despite such nonlinearities. This paper addresses these challenges by employing dynamic feedback linearization, which extends classical feedback linearization by incorporating dynamic compensators to transform nonlinear systems into linear systems via appropriate state, feedback, and compensator transformations. The linear system can be altered to incorporate classical control techniques in a simpler form to analyze. Moreover, the stability of the transformed system will be analyzed extensively based on Lyapunov quadratic functions and Linear Matrix Inequalities (LMIs) to come up with a robust and systematic toolbox for stability analysis. Additionally, its applicative effectiveness to an autonomous vehicle model will demonstrate its usefulness for addressing practical CPS scenarios. This work develops novel knowledge regarding the behavior of nonlinear systems in the framework of stability, and this is crucial for the design and deployment of CPSs in complex applications.