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Results for “asymptotic stability”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1971

Asymptotic stability properties of linear Volterra integrodifferential equations.

The Liapunov stability properties of solution to a certain system of Volterra integrodifferential equations is studied. Various types of Liapunov stability are defined; the definitions are natural extensions of the corresponding notions for ordinary differential equations. Necessary and sufficient conditions, in general, for uniform stability and uniform asymptotic stability are obtained in the form of a theorem. Connections between the stability of the system studied and the stability properties of a related Volterra integrodifferential equation with infinite memory are examined. Sufficient conditions in order that the trivial solution to the system studied be stable, uniformly stable, asymptotically stable, or uniformly asymptotically stable are derived.

Miller, R. K.↗
NASA NTRS1973

Asymptotic stability and instability of large-scale systems

The purpose of this paper is to develop new methods for constructing vector Lyapunov functions and broaden the application of Lyapunov's theory to stability analysis of large-scale dynamic systems. The application, so far limited by the assumption that the large-scale systems are composed of exponentially stable subsystems, is extended via the general concept of comparison functions to systems which can be decomposed into asymptotically stable subsystems. Asymptotic stability of the composite system is tested by a simple algebraic criterion. By redefining interconnection functions among the subsystems according to interconnection matrices, the same mathematical machinery can be used to determine connective asymptotic stability of large-scale systems under arbitrary structural perturbations.

Grujic, L. T.↗
DOE OSTI2019

Decentralized Voltage and Power Control of Multi-Machine Power Systems With Global Asymptotic Stability

Maintaining power system stability is becoming urgent due to the large-scale interconnection of power grids and the high penetration of uncertain renewable energy sources. The excitation control and governor control of synchronous generators have been considered as two crucial measures for enhancing the power system stability. However, a major challenge is to simultaneously achieve global asymptotic stability (GAS), voltage regulation (VR), and power regulation (PR) in the excitation and governor control. In this paper, a Lyapunov-based decentralized control (LBC) is proposed to address this challenge. The time-derivative of the Lyapunov function is designed by the feedback control of synchronous generators in order to guarantee GAS. VR and PR are ensured by considering voltage and power deviations as the feedback variables. The simulation results on the New-England ten-machine power system validate the effectiveness of the proposed LBC in improving power system transient stability and simultaneously achieving VR and PR. Although the proportional-integral- and power system stabilizer-based control can also perform VR and PR, the proposed control has much better dynamic performance and can more significantly improve the system transient stability.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2018

On a Method of Study of Specific Asymptotic Stability of Solutions to a Sixth-Order Linear Integrodifferential Volterra Equation

We state sufficient conditions of the asymptotic stability on the semi-axis of solutions to a linear, homogeneous, sixth-order integrodifferential Volterra-type equation in the case where solutions of the corresponding linear, homogeneous, sixth-order differential equation are asymptotically unstable. We also present a new method and an illustrating example.

97 MATHEMATICS AND COMPUTING↗