Exponential Estimates of a Class of Time–Delay Nonlinear Systems with Convex Representations

Abstract

This work introduces a novel approach to stability and stabilization of nonlinear systems with delayed multivariable inputs; it provides exponential estimates as well as a guaranteed cost of the system solutions. The result is based on an exact convex representation of the nonlinear system which allows a Lyapunov-Krasovskii functional to be applied in order to obtain sufficient conditions in the form of linear matrix inequalities. These are efficiently solved via convex optimization techniques. A real-time implementation of the developed approach on the twin rotor MIMO system is included.

LMI-Based Analysis and Stabilization of Nonlinear Descriptors with Multiple Delays via Delayed Nonlinear Controller Schemes

“…is technique has also been applied to a class of nonlinear TDS; for instance, in [58,59], sufficient LMI conditions are proposed; in [60], uncertain TS systems are considered; in [61], sufficient LMI conditions have been given for a class of nonlinear systems. A larger family of functionals is explored in [62].…”

A Review of Convex Approaches for Control, Observation and Safety of Linear Parameter Varying and Takagi-Sugeno Systems

“…The idea of unifying these two paradigms under a single name is not new, as it was originally proposed in Ref. [36] and retaken in Refs. [37][38][39][40].…”

Contribuciones al estudio de sistemas lineales con retardos: el enfoque de funcionales de tipo completo

“…El uso de funcionales de tipo prescrito ha sido objeto de intensa investigación en las décadas pasadas: la propuesta de funcionales parametrizadas que se derivan a lo largo de las trayectorias del sistema en lazo cerrado conduce a condiciones suficientes expresadas como desigualdades lineales o bilineales matriciales que se resuelven simultáneamente para los parámetros de la funcional y las ganancias del control. Este enfoque es sumamente útil en los problemas de síntesis ya que es posible formular numerosos problemas de control y encontrar soluciones gracias a los grados de libertad de sus parámetros (Ramírez Jerónimo et al, 2020;Ramírez et al, 2015;Villafuerte et al, 2011Villafuerte et al, , 2013Ramírez et al, 2018). En un contexto de análisis, el método es más limitado ya que las condiciones son suficientes, y no hay garantía de que, dado un sistema estable, existan valores de los parámetros de la funcional de forma prescrita que satisfagan los teoremas de estabilidad.…”