← 研踪 PaperTrailarXiv:2611.13048 · v1
Reliable Computation of the $L_{\infty}$-Norm of Linear Time-Invariant Systems Depending on One Parameter
首次提交 2026-11-09 21:59
版本更新 2026-11-09 21:59
雷达观测 2026-11-11 11:05
摘要
The -norm of a linear time-invariant system is a central quantity in robust control, used in robust stability tests, stability margins, and controller design. Physical models depend on parameters, such as masses, stiffnesses, or gains, so the -norm becomes a function of these parameters. This computation reduces to studying the real critical points of a plane algebraic curve whose coefficients depend on the parameters. Previous approaches based on cylindrical algebraic decomposition describe the -norm on the whole parameter space, but their cost grows very quickly with the number of parameters. In this paper, we propose instead to compute a generic parametrisation of the solutions, valid outside an explicitly characterised set of non-generic parameter values. In the case of one parameter, this parametrisation is obtained by interpolation from a certified solver for the non-parametric case. The resulting algorithm is fully certified, relying on a priori bounds and multimodular computations rather than on Gröbner bases. It is illustrated on examples from the robust control literature.
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v1 · 2026-11-09 21:59 · 最新观测版本
Reliable Computation of the $L_{\infty}$-Norm of Linear Time-Invariant Systems Depending on One Parameter
The -norm of a linear time-invariant system is a central quantity in robust control, used in robust stability tests, stability margins, and controller design. Physical models depend on parameters, such as masses, stiffnesses, or gains, so the -norm becomes a function of these parameters. This computation reduces to studying the real critical points of a plane algebraic curve whose coefficients depend on the parameters. Previous approaches based on cylindrical algebraic decomposition describe the -norm on the whole parameter space, but their cost grows very quickly with the number of parameters. In this paper, we propose instead to compute a generic parametrisation of the solutions, valid outside an explicitly characterised set of non-generic parameter values. In the case of one parameter, this parametrisation is obtained by interpolation from a certified solver for the non-parametric case. The resulting algorithm is fully certified, relying on a priori bounds and multimodular computations rather than on Gröbner bases. It is illustrated on examples from the robust control literature.
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