Robust MIMO LQR Control with Integral Action for Differential Drive Robots: A Lyapunov-Cost Function Approach

Abstract

This study introduces an LQR-enhanced MIMO state feedback system with integral action to ensure precise trajectory tracking by eliminating persistent offsets. Unlike standard LQR methods, the proposed approach integrates integral action without requiring separate disturbance observers, reducing computational complexity for embedded systems. A unique Lyapunov-based analysis, leveraging the LQR cost function, confirms stability with uniform ultimate boundedness despite external perturbations. MATLAB simulations reveal RRMSE values under 10% for longitudinal speed and yaw rate, even when subjected to step and stochastic disturbances. This method outperforms conventional PID and LQR-feedforward techniques, offering a lightweight, efficient solution for DDWMR applications in industrial logistics, field exploration, and real-time robotic systems.