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Leyes de Conmutación Novedosas para Sistemas No Lineales de Tiempo Retardado Conmutados y Aplicaciones a Redes
IEEE transactions on cybernetics
|January 6, 2026
Resumen
Este estudio introduce nuevas leyes de conmutación, densidad de conmutación promedio y densidad de conmutación promedio dependiente del modo, para sistemas no lineales de tiempo retardado. Estos nuevos métodos mejoran el análisis de estabilidad y reducen el conservadurismo en sistemas conmutados.
Área de la Ciencia:
- Ingeniería de Sistemas de Control
- Dinámica No Lineal
- Teoría de Sistemas
Sus antecedentes:
- Los sistemas no lineales de tiempo retardado conmutados (SNTDS) requieren un diseño eficaz de la ley de conmutación para la estabilidad.
- Los métodos existentes, como el tiempo de permanencia y el ADT, pueden no capturar completamente la dinámica de conmutación.
- El conservadurismo en los criterios de estabilidad limita las aplicaciones prácticas.
Objetivo del estudio:
- Proponer nuevas leyes de conmutación para SNTDS: densidad de conmutación promedio (ASD) y densidad de conmutación promedio dependiente del modo (MDASD).
- Desarrollar criterios de estabilidad relajados para SNTDS bajo estas nuevas leyes de conmutación.
- Aplicar los métodos propuestos a redes neuronales conmutadas.
Principales métodos:
- Introducción de ASD y MDASD para caracterizar la frecuencia de conmutación.
- Construcción de múltiples funciones de Lyapunov-Razumikhin.
- Utilización de desigualdades integrales relajadas y enfoques basados en trayectorias.
- Aplicación al análisis de estabilidad de redes neuronales conmutadas.
Principales resultados:
- Se derivan nuevos criterios de estabilidad para SNTDS bajo ASD y MDASD.
- Los criterios propuestos son menos conservadores que los métodos existentes.
- Se demuestra la efectividad a través de la aplicación a redes neuronales conmutadas.
- Validación a través de dos ejemplos ilustrativos.
Conclusiones:
- Las leyes de conmutación ASD y MDASD propuestas ofrecen una representación más precisa de la dinámica de conmutación.
- Los criterios de estabilidad desarrollados mejoran la garantía de estabilidad del sistema y reducen el conservadurismo.
- El enfoque es eficaz para analizar redes neuronales conmutadas y otros SNTDS.
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