Field Programmable Gate Array (FPGA)-Based Architecture for Real-Time Lyapunov Stability Analysis in Autonomous Control Systems

This paper presents a novel FPGA-based architecture for real-time Lyapunov stability analysis in autonomous control systems, designed to ensure rapid and efficient stability assessment under dynamic conditions. The proposed architecture leverages parallel processing capabilities of FPGA to implement the Lyapunov function V ( x ) = x ∧ TPx with matrix P chosen for system-specific stability requirements. The design achieves a processing latency of 2.3 μ s per stability check, significantly reducing response time compared to traditional CPU implementations, which average 12.8 us under similar conditions. Key features include a pipelined structure optimized for low-latency matrix-vector multiplication, numerical derivative calculations of V(x) , and threshold-based decision logic for real-time stability assessment. Implemented on a Xilinx Virtex-7 FPGA, the architecture utilizes 87% of available DSP slices for parallel multiplication and addition, achieving a throughput of 250 stability checks per millisecond. This real-time capability is essential for high-speed applications, such as autonomous vehicles and adaptive robotic systems, where stability monitoring must be continuous and immediate. Experimental results indicate that the FPGA-based system outperforms CPU-based stability analysis by 80% in speed while maintaining an accuracy of 99.6% in stability assessment, as verified against a software-based Lyapunov stability model. The proposed architecture demonstrates potential for scalability, allowing adaptability to higher-dimensional systems with only a 15% increase in resource utilization per additional state variable. This study highlights the efficacy of FPGA architectures in enhancing the responsiveness and reliability of autonomous control systems through real-time stability analysis.