H_∞ Control of Time-Delay Systems Based on the CHsCTA Method

This study proposes a control method based on the Chebyshev spectral continuous time approximation (CHsCTA) for solving the H_∞ control design problem of time-delay systems. The core innovation involves adopting CHsCTA technology and constructing appropriate augmented matrices to reconfigure the original time-delay system into a transformed system that is free of time delay. Subsequent control design is performed on the transformed system, yielding bilinear matrix inequalities (BMIs) for controller determination. Finally, an efficient iterative algorithm is constructed to solve the BMIs problem and obtain the H_∞ controller by combining the cone complementarity linearization (CCL) approach. Numerical results demonstrate that compared with the traditional Lyapunov-Krasovskii (L-K) functional-based algorithms, the proposed approach achieves significant improvements in reducing conservatism and enhancing H_∞ control performance.