Practical stability and stabilization of a class of nonlinear neutral type time delay systems with multiple delays: BMI’s approaches

Lyapunov matrix‐based method to global robust practical exponential r‐stability for a class of delayed continuous‐time nonlinear systems: Theory and applications

“…Remark In this section, we have presented a Lyapunov matrix‐based LKF method to set up a global robust practical exponential $$$ r $$$‐stable criterion for delayed continuous‐time nonlinear systems. Different from commonly used LKF method, 29‐31 the proposed method is based on the complete‐type LKF $$$ V\left(\cdotp \right) $$$ defined in (5). Therein, the part $$$ {V}_0\left(\cdotp \right) $$$ has been used to investigate necessary and sufficient conditions for stability of several time‐delay systems, 36 while the part $$$ {V}_3\left(\cdotp \right) $$$ is proposed in this paper for the first time, and is necessary to solve the control problems under consideration.…”

“…The analysis of practical stability for nonlinear systems has become one of the important research topics in the field of control theory and its applications. Recent years, this subject has achieved a number of excellent research results, see References 20‐24 for delay free systems, and References 25‐31 for time‐delay systems. Stamova 27 used the vector Lyapunov function method and the differential inequalities of piecewise continuous functions to study the practical stability of solutions of impulsive nonlinear functional differential equations.…”

“…Echi 29 studied the observer design problem for a class of time‐delay nonlinear systems written in triangular form, and sufficient conditions for the practical stability of the error system are given by applying Lyapunov–Krasovskii functional (LKF) method. By applying the LKF method, Villafuerte et al 30 studied the practical stability of neutral time‐delay systems. Zhao 31 used the Lyapunov function method and the comparison principle to present sufficient conditions for the practical stability of stochastic systems with Markovian jump parameters and time‐varying delays.…”

Mean square stability of linear stochastic neutral‐type time‐delay systems with multiple delays

“…Condition (13) has been frequently used in the literature. 22,[37][38][39][40][41][42] Motivated by our recent study, 34 we impose an alternative assumption on D(x t ) (or ).…”

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.…”