In this research work, a six-term 3-D novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities has been proposed, and its qualitative properties have been detailed. The Lyapunov exponents of the novel jerk system are obtained as L 1 = 0.07765, L 2 = 0, and L 3 = −0.87912. The Kaplan-Yorke dimension of the novel jerk system is obtained as D KY = 2.08833. Next, an adaptive backstepping controller is designed to stabilize the novel jerk chaotic system with two unknown parameters. Moreover, an adaptive backstepping controller is designed to achieve complete chaos synchronization of the identical novel jerk chaotic systems with two unknown parameters. Finally, an electronic circuit realization of the novel jerk chaotic system using Spice is presented in detail to confirm the feasibility of the theoretical model.
A hyperjerk system is a dynamical system, which is modelled by an nth order ordinary differential equation with n 4 describing the time evolution of a single scalar variable. Equivalently, using a chain of integrators, a hyperjerk system can be modelled as a system of n first order ordinary differential equations with n 4. In this research work, a 4-D novel hyperchaotic hyperjerk system has been proposed, and its qualitative properties have been detailed. The Lyapunov exponents of the novel hyperjerk system are obtained asThe Kaplan-Yorke dimension of the novel hyperjerk system is obtained as D KY = 3.1573. Next, an adaptive backstepping controller is designed to stabilize the novel hyperjerk chaotic system with three unknown parameters. Moreover, an adaptive backstepping controller is designed to achieve global hyperchaos synchronization of the identical novel hyperjerk systems with three unknown parameters. Finally, an electronic circuit realization of the novel jerk chaotic system using SPICE is presented in detail to confirm the feasibility of the theoretical hyperjerk model.
For the last five decades, there has been great interest in the control literature in deriving reduced order models for large-scale linear control systems. Such reduced order models have great applications in science, engineering and industry. In this paper, we have studied the problem of designing linear functional observers for large-scale linear discrete-time control systems and derived some new results, viz. necessary and sufficient conditions for the reduced order linear functional observer for discrete-time linear control systems. We have also established a separation principle for implementation of an observer-based feedback stabilization scheme. A simple algorithm has been provided for the ready implementation of the proposed linear functional observer. A numerical example using MATLAB has been provided to illustrate the new design procedure.
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