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Absolute stability criteria for large-scale Lurie direct control systems with time-varying coefficients.

ABSTRACT: The absolute stability of large-scale Lurie direct control systems with time-varying coefficients is investigated. Based on the decomposition method for large-scale systems and technique of the nonsingular M-matrix, a suitable scalar Lyapunov function as a weighted sum is constructed. By estimating its total time derivative, some absolute stability criteria and practical corollaries are derived. Furthermore, the results are extended to multiple nonlinearities. The salient feature of this paper is that the criteria which we propose allow for the situation that the norms of time-varying coefficients are unbounded. The main idea of the methodology is that even if the coefficients are norm-unbounded, by restricting their relative magnitude, the problem of negative definiteness for the derivative can also be changed into the problem of stability for a constant matrix. Finally, some numerical examples are included to illustrate the effectiveness of the proposed criteria.

SUBMITTER: Liao F

PROVIDER: S-EPMC4032661 | biostudies-other | 2014

REPOSITORIES: biostudies-other

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Project description:Measuring whole-brain functional connectivity patterns based on task-free ('resting-state') spontaneous fluctuations in the functional MRI (fMRI) signal is a standard approach to probing habitual brain states, independent of task-specific context. This view is supported by spatial correspondence between task- and rest-derived connectivity networks. Yet, it remains unclear whether intrinsic connectivity observed in a resting-state acquisition is persistent during task. Here, we sought to determine how changes in ongoing brain activation, elicited by task performance, impact the integrity of whole-brain functional connectivity patterns (commonly termed 'resting state networks'). We employed a 'steady-states' paradigm, in which participants continuously executed a specific task (without baseline periods). Participants underwent separate task-based (visual, motor and visuomotor) or task-free (resting) steady-state scans, each performed over a 5-minute period. This unique design allowed us to apply a set of traditional resting-state analyses to various task-states. In addition, a classical fMRI block-design was employed to identify individualized brain activation patterns for each task, allowing us to characterize how differing activation patterns across the steady-states impact whole-brain intrinsic connectivity patterns. By examining correlations across segregated brain regions (nodes) and the whole brain (using independent component analysis) using standard resting-state functional connectivity (FC) analysis, we show that the whole-brain network architecture characteristic of the resting-state is comparable across different steady-task states, despite striking inter-task changes in brain activation (signal amplitude). Changes in functional connectivity were detected locally, within the active networks. But to identify these local changes, the contributions of different FC networks to the global intrinsic connectivity pattern had to be isolated. Together, we show that intrinsic connectivity underlying the canonical resting-state networks is relatively stable even when participants are engaged in different tasks and is not limited to the resting-state.

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Absolute stability criteria for large-scale Lurie direct control systems with time-varying coefficients.

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