This study addresses the adaptive synchronization of Rössler and Chua circuit systems with unknown parameters. By using Lyapunov stability theory the adaptive synchronization law with a single-state variable feedback is derived, such that the trajectory of the two systems are globally stabilized to an equilibrium point of the uncontrolled system (globally stable means that the method of the sol...

This paper addresses functional projective lag synchronization of Lorenz system with four unknown parameters, where the output of the master system lags behind the output of the slave system proportionally. For this purpose, an adaptive control law is proposed to make the states of two identical Lorenz systems asymptotically synchronize up. Based on Lyapunov stability theory, a novel criterion ...

This paper investigates the global chaos synchronization of identical hyperchaotic Xu systems (Xu, Cai and Zheng, 2009) by sliding mode control. The stability results derived in this paper for the complete synchronization of identical hyperchaotic Xu systems are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the sliding mode co...

In this paper, a robust local controller has been designed to balance the power for distributed energy resources (DERs) in an islanded microgrid. Three different DER types are considered in this study; photovoltaic systems, battery energy storage systems, and synchronous generators. Since DER dynamics are nonlinear and uncertain, which may destabilize the power system or decrease the performanc...

This paper describes the design of an adaptive direct control scheme for a class of nonlinear systems. The architecture is based on a fuzzy inference system (FIS) of Takagi Sugeno (TS) type to approximate a feedback linearization control law. The parameters of the consequent part of the fuzzy system are adapted and changed according to a law derived using Lyapunov stability theory. The asymptot...

First, this paper introduces a seven-term novel 3-D chaotic system and discusses its qualitative properties. The proposed system is a seven-term novel polynomial chaotic system with three quadratic nonlinearities. The Lyapunov exponents of the novel chaotic system are obtained as L1 = 3.3226, L2 = 0 and L3 = –30.3406. The maximal Lyapunov exponent (MLE) for the novel chaotic system is obtained ...

This paper investigates the anti-synchronization of identical Pan systems (Pan, Xu and Zhou, 2010) by sliding mode control. The stability results derived in this paper for the anti-synchronization of identical Pan systems are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the sliding mode control method is very effective and co...

This paper studies a novel class of feedback control systems of impulsive fractional differential equations on networks (FCSIFDENs). By combining some graph theory and the Lyapunov method, we provide a systematic method for constructing a global Lyapunov function for FCSIFDENs. Consequently, a new global asymptotic stability principle and a new global Mittag–Leffler stability principle, which h...

This paper investigates the global chaos synchronization of identical hyperchaotic Lü systems (Chen, Lu, Lü and Yu, 2006) by sliding mode control. The stability results derived in this paper for the complete synchronization of identical hyperchaotic Lü systems are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the sliding mode ...

This paper investigates the anti-synchronization of identical hyperchaotic Xu systems (Xu, Cai and Zheng, 2009) via sliding mode control. The stability results derived in this paper for the anti-synchronization of identical hyperchaotic Xu systems are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the sliding mode control metho...