Stability and Stabilization of the Fractional-order Power System with Time Delay
Abstract : This brief investigates the problems of stability and stabilization of the fractional-order power system with time delay. The models of the fractional-order nonlinear and linearized delayed power system are established, respectively. Based on the theory of the fractional calculus and the Lyapunov functional technique, the relevant stability criteria are obtained. Meantime, new Lyapunov functionals are constructed, and the free-weighing matrix technique is introduced to reduce the conservatism of the criteria. The developed results can also be further extended to other similar nonlinear circuit systems. At last, effectiveness of the obtained results is demonstrated by simulation. Besides, simulation results indicate that the fractional-order model of the power system can more accurately describe the chaos phenomenon than the corresponding integer-order model, and the designed controller is valid.
? Our work presents a novel methodology to study the FTS of FOTDSs using the fixed point approach.
? We will exploite a fixed point theorem in order to study finite time stability for FOTDSs.
? In this work, the robust FTS of FOTDSs with disturbances was studied.
? By proposing an approach based on the fixed point theory we have obtained a new sufficient condition for the robust FTS of such system.
? Furthermore, based on the generalized Gronwall inequality, Naifar et al. in have described a FTS result of the FOTDSs using the Caputo Fractional Derivative (CFD).
? The problem of sufficient conditions that enable system trajectories to stay within the a priori given sets for a particular class of (non)linear (non)autonomous fractional order time-delay systems has been examined.
? In the field of fractional-order control systems, there are many challenging and unsolved problems related to the stability theory such as robust stability, bounded input – bounded output stability, internal stability, root-locus, robust controllability, robust observability, etc.
? In spite of intensive research, the stability of fractional order (time delay) systems remains an open problem
• In this article, a novel Finite Time Stability (FTS) scheme for FractionalOrder Time Delayed Systems (FOTDSs) is proposed.
• Fractional-Order Systems (FOS) can be defined as nonlinear systems that are modeled by Fractional Differential Equations (FDEs), carried out with non-integer derivatives. Indeed, such system dynamics.
• Indeed, such system dynamics are described by fractional derivatives.
• Integrals and derivatives of fractional orders are used to demonstrate objects that can be described by power-law long-range dependence or power-law nonlocality or fractal properties
? A system could be stable but still completely useless because it possesses undesirable transient performances.
? In particular, pure delays are often used to ideally represent the effects of transmission, transportation, and inertial phenomena.
? This is because these systems have only limited time to receive information and react accordingly.
? Such a system cannot be described by purely differential equations, but has to be treated with differential difference equations or the so-called differential equations with difference variables.
? Time invariant sets, used as the bounds of system trajectories, are assumed to be open, connected and bounded.
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