Nonfragile H∞ Static Output Feedback Control for Time-Delay Systems

This study addresses the nonfragile static output feedback control problem in time-delay systems and introduces an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control strategy developed through the Chebyshev spectral continuous time approximation (CHsCTA). First, the time-delay system is transformed into a delay-free representation using the CHsCTA method. Subsequently, a control scheme is designed for this reformulated system, which leads to the derivation of bilinear matrix inequalities (BMIs) that determine the controller parameters. The proposed post-transformation design strategy significantly simplifies the control synthesis process. Finally, an iterative algorithm based on the Cone Complementarity Linearization (CCL) technique is developed to calculate the minimal <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance index and feedback gain matrix, thereby ensuring robust stability and disturbance rejection capability in the closed-loop system. Numerical simulations conducted on a liquid rocket engine propulsion system confirm the effectiveness of the proposed approach. Compared with conventional Lyapunov-Krasovskii functional-based techniques, the proposed method achieves a lower <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance index.