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Estabilidad de sistemas estocásticos no lineales bajo control impulsivo desencadenado por eventos con impulsos de

Bing Shang¹, Jin-E Zhang¹

¹School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China.

Mathematical biosciences and engineering : MBE

|September 3, 2025

Resumen

Este estudio introduce el control impulsivo desencadenado por eventos (ETIC) para sistemas estocásticos no lineales con retrasos. Nuevos mecanismos aseguran la estabilidad y evitan el comportamiento de Zeno, validado por LMI y ejemplos numéricos.

Área de la Ciencia:

Teoría de control
Sistemas no lineales
Sistemas estocásticos

Sus antecedentes:

Los sistemas de control impulsivos son cruciales para la gestión de dinámicas complejas.
Los retrasos distribuidos y la estocasticidad presentan importantes desafíos de estabilidad.
El control impulsivo activado por eventos (ETIC) ofrece una transmisión de datos eficiente.

Objetivo del estudio:

Investigar la estabilidad de sistemas estocásticos no lineales con impulsos de retardo distribuido bajo ETIC.
Proponer nuevos mecanismos desencadenados por eventos continuos y periódicos (ETM) que eviten el comportamiento de Zeno.
Establecer condiciones suficientes para la estabilidad uniforme del momento p-ésimo (p-US) y la estabilidad exponencial del momento p-ésimo (p-ES).

Principales métodos:

Método de Lyapunov y inducción matemática para el análisis de estabilidad.
Desarrollo de mecanismos desencadenados por eventos continuos y periódicos (ETM).
Enfoque de desigualdad de matriz lineal (LMI) para el diseño conjunto de ETM y ganancias de control.

Principales resultados:

Condiciones suficientes derivadas para garantizar p-US y p-ES en sistemas con impulsos de retardo distribuido.
Los ETM propuestos eliminan efectivamente el comportamiento de Zeno.
Aplicación exitosa a sistemas estocásticos no lineales, demostrando la viabilidad a través de ejemplos numéricos.

Conclusiones:

El marco ETIC propuesto proporciona un método sólido para estabilizar sistemas estocásticos no lineales con retrasos distribuidos.
El diseño conjunto que utiliza LMI garantiza un control y una estabilidad efectivos.
Las simulaciones numéricas confirman la aplicabilidad práctica y la eficacia de los resultados teóricos.

Palabras clave:

Impulsos de retardo distribuido Control impulsivo desencadenado por un evento Sistema estocástico no lineal Estabilidad

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