🤖 AI Summary
研究用符号计算方法精确求解有限维线性系统的L∞范数，比较了Sturm-Habicht序列、RUR和CAD等方法与数值法的优劣，突出符号法在参数化情况下的精度优势。
📝 Abstract
The computation of the $L_infty $-norm is an important issue in $H_{infty}$ control, particularly for analyzing system stability and robustness. This paper focuses on symbolic computation methods for determining the $L_{infty} $-norm of finite-dimensional linear systems, highlighting their advantages in achieving exact solutions where numerical methods often encounter limitations. Key techniques such as Sturm-Habicht sequences, Rational Univariate Representations (RUR), and Cylindrical Algebraic Decomposition (CAD) are surveyed, with an emphasis on their theoretical foundations, practical implementations, and specific applicability to $ L_{infty} $-norm computation. A comparative analysis is conducted between symbolic and conventional numerical approaches, underscoring scenarios in which symbolic computation provides superior accuracy, particularly in parametric cases. Benchmark evaluations reveal the strengths and limitations of both approaches, offering insights into the trade-offs involved. Finally, the discussion addresses the challenges of symbolic computation and explores future opportunities for its integration into control theory, particularly for robust and stable system analysis.