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α-stability and α-synchronization for fractional-order neural networks

Juan Yu1, Cheng Hu, Haijun Jiang

  • 1College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang, PR China. yujuanseesea@163.com

Neural Networks : the Official Journal of the International Neural Network Society
|September 8, 2012
PubMed

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Multimachine Stability01:25

Multimachine Stability

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In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
Stability01:28

Stability

The time response of a linear time-invariant (LTI) system can be divided into transient and steady-state responses. The transient response represents the system's initial reaction to a change in input and diminishes to zero over time. In contrast, the steady-state response is the behavior that persists after the transient effects have faded.
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Pole and System Stability

The transfer function is a fundamental concept representing the ratio of two polynomials. The numerator and denominator encapsulate the system's dynamics. The zeros and poles of this transfer function are critical in determining the system's behavior and stability.
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BIBO stability of continuous and discrete -time systems

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First-order systems, such as RC circuits, are foundational in understanding dynamic systems due to their straightforward input-output relationship. Analyzing their responses to different input functions under zero initial conditions reveals significant insights into system behavior.
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