Lyapunov-Based $\mathcal{L}_2$-Stable PI-Like Control of a Four-Wheel Independently Driven and Steered Robot

In this letter, Lyapunov-based synthesis of a PI-like controller is proposed for $\mathcal{L}_2$-stable motion control of an independently driven and steered four-wheel mobile robot. An explicit, structurally verified model is used to enable systematic controller design with stability and performance guarantees suitable for real-time operation. A Lyapunov function is constructed to yield explicit bounds and $\mathcal{L}_2$ stability results, supporting feedback synthesis that reduces configuration dependent effects. The resulting control law maintains a PI-like form suitable for standard embedded implementation while preserving rigorous stability properties. Effectiveness and robustness are demonstrated experimentally on a real four-wheel mobile robot platform.