Stability analysis and $ {H_\infty } $ control for rough singular systems with Pythagorean functions

Li Li; Xiaolin Zhao; Li Li; Xiaolin Zhao

doi:10.3934/math.20261133

AIMS Mathematics

2026, Volume 11, Issue 9: 28452-28469. doi: 10.3934/math.20261133

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Research article Special Issues

Stability analysis and $ {H_\infty } $ control for rough singular systems with Pythagorean functions

Li Li ^,,
Xiaolin Zhao

College of Mathematical Sciences, Bohai University, Jinzhou 121000, China

Received: 02 July 2026 Revised: 20 August 2026 Accepted: 26 August 2026 Published: 07 September 2026
MSC : 93C05, 03E72, 93C42

This paper integrated Pythagorean fuzzy sets, intuitionistic $ \left(\lambda, \eta \right) $‑function rough sets, and singular systems to develop rough singular systems of Pythagorean functions (RSSPFs) and investigate its $ {H_\infty } $ control. Focusing on uncertain information, RSSPFs first adopted Pythagorean fuzzy sets to accurately model uncertainties. Based on rough set theory, RSSPFs were decomposed into a lower‑approximation set subsystem and a boundary set subsystem. By combining these two subsystems within the $ {H_\infty } $ control framework for singular systems, a closed‑loop control system was constructed to suppress disturbances. Applied to the path‑tracking problem of autonomous vehicles, simulation experiments showed that the $ {H_\infty } $ control for RSSPFs ensured the asymptotic stability of all subsystems, and effectively balanced the tracking accuracy and robustness.
- $ {H_\infty } $ control for rough singular systems of Pythagorean functions,
- fuzzy rough set,
- admissibility
Citation: Li Li, Xiaolin Zhao. Stability analysis and $ {H_\infty } $ control for rough singular systems with Pythagorean functions[J]. AIMS Mathematics, 2026, 11(9): 28452-28469. doi: 10.3934/math.20261133

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Abstract

This paper integrated Pythagorean fuzzy sets, intuitionistic $ \left(\lambda, \eta \right) $‑function rough sets, and singular systems to develop rough singular systems of Pythagorean functions (RSSPFs) and investigate its $ {H_\infty } $ control. Focusing on uncertain information, RSSPFs first adopted Pythagorean fuzzy sets to accurately model uncertainties. Based on rough set theory, RSSPFs were decomposed into a lower‑approximation set subsystem and a boundary set subsystem. By combining these two subsystems within the $ {H_\infty } $ control framework for singular systems, a closed‑loop control system was constructed to suppress disturbances. Applied to the path‑tracking problem of autonomous vehicles, simulation experiments showed that the $ {H_\infty } $ control for RSSPFs ensured the asymptotic stability of all subsystems, and effectively balanced the tracking accuracy and robustness.

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