Stability analysis and robust control of cyber-physical systems: integrating Jacobian linearization, Lyapunov methods, and linear quadratic regulator control via LMI techniques

Abstract

Stability issues in cyber-physical systems (CPS) arise from the challenging effects of nonlinear dynamics relation to multi-input, multi-output systems. This research proposed a robust control framework that combines Jacobian linearization, Lyapunov stability analysis, and linear quadratic regulator (LQR) control via linear matrix inequalities (LMIs). The robust methodology does the following: it applies linearization on the dynamics of the CPS; it establishes the stability of the system using Lyapunov functions and LMIs; and it designs an LQR controller. The proposed framework was validated through a comparison between the behavior of a linearized and nonlinear model. The autonomous vehicle application showed: a settling time of 20 seconds; an overshoot of 3.8187%; and a steady-state error of 2.688×10⁻⁷. The proposed framework is robustly demonstrated and has applications to areas in automation and smart infrastructure. Future work includes optimizing the design of weighting matrices and developing adaptive control features.