Synchronization of non‐linear systems with disturbances subjected to dead‐zone and saturation characteristics in control input using DMVT approach

Abstract

A synchronization criterion for chaotic non-linear systems with disturbances is discussed in this paper, which ensures effective synchronization between the systems even with dead-zone and saturation non-linearities in the controller input. The system non-linearities are addressed with the help of Differential Mean Value Theorem (DMVT), rather than treating them as Lipschitz. The reformulation of non-linearity terms through DMVT provides the Linear Matrix Inequality (LMI) conditions for controller design to be less restrictive. Lyapunov stability theory and LMI formulations are used for ensuring asymptotic stability of the overall system under input dead-zone and saturation. Moreover, an adaptive parameter is used in the controller to reduce the effect of norm-bounded disturbances. Extensive simulation results are presented at the end to ensure the efficacy of the proposed scheme. KEYWORDS adaptive controller, dead-zone and saturation non-linearity, differential mean value theorem (DMVT), linear matrix inequality (LMI)

Synchronization of Chaotic Systems with Dead Zones via Fuzzy Adaptive Variable-Structure Control

“…Previously, many researchers have used various methods to settle the synchronization problem of the nonlinear systems, that is, the control input with dead zones. For instance, using Laplace transform approach to settle synchronization of nonlinear systems with disturbances subjected to dead-zone and saturation characteristics in control input was studied in [32], projective synchronization of Chua's chaotic systems that control input has dead zones was studied in [33,34], and using adaptive fuzzy sliding mode control to deal with unknown nonlinear chaotic gyros synchronization with unknown dead-zone input was studied in [35].…”

“…In this paper, we put forward a fuzzy adaptive variablestructure synchronization scheme to manage the dead-zone nonlinearity and analyze the synchronization properties of chaotic systems. Comparing the related works, for example, [26,32,34], the contribution of this works consists in the following: (1) Input nonlinearity is considered in this paper. However, it is not considered in the above literature.…”

“…However, it is not considered in the above literature. (2) Compared with [26,32], the assumptions of this work are more realistic.…”

Variance‐constrained H∞ synchronization control of discrete time‐delayed complex dynamical networks: An intermittent pinning approach

“…In particular, the analysis of complex network synchronization has been attracted more extensive attention. Up to now, a rich body of literature about synchronization issues have been reported [1‐3]. It is now well recognized that some network phenomena are existence in the process of signal transmission, the typical one is time delay, which is ubiquitous in all kinds of systems including differential equations with non‐monotone bistable nonlinearities [4], food‐chain model [5], neutral‐type stochastic Markovian jump static neural networks [6], and so on.…”

Robust Observer Design for Uncertain Lipschitz Nonlinear Systems Based on Differential Mean Value Theorem: Application to Induction Motors

“…Despite the importance of sensitivity to parametric variations in stability studies, but the previous works (Hammoudi et al 2014;Zeghib et al 2019) did not incorporate them due to the additional complexity and its implication (Dinesh and Sharma 2019). The first discussions about the problem of robust observer design for a class of Lipschitz nonlinear systems in the presence of disturbance and model uncertainties go back to the works of de Souza et al (1993).…”