Real stability radii of linear time-invariant time-delay systems

Hu, Guangdi; Davison, E.J.

doi:10.1016/s0167-6911(03)00155-5

Cited by 31 publications

(43 citation statements)

References 17 publications

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“…If only real entries of the perturbation matrices δM, δC and δK are allowed, then the corresponding real stability radius can be calculated following [21] and [13] as…”

Section: Real Stability Radiusmentioning

confidence: 99%

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Robust stability analysis of machining operations

Hajdu

Insperger

Stépàn

2016

Int J Adv Manuf Technol

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Prediction of machine tool chatter requires the characterization of dynamic of the machine-toolworkpiece system by means of frequency response functions (FRFs). Uncertainties of the measured FRFs result in uncertainties of the calculated stability diagrams, therefore robustness of stability prediction against parameter perturbations is of high importance. Although there exist methods to determine robust stability in terms of stability radii, these methods either give a conservative estimate of the real uncertainties or are limited to perturbations of a few modal parameters, only. In this paper, a frequency-domain approach is presented to determine robust stability boundaries using the measured FRFs directly without any modal parameter identification. The method is based on an envelope fitting around the measured FRFs combined with some considerations of the single-frequency method. The application of the method is demonstrated in case of a turning operation, where the machine tool structure is characterized by a series of FRF measurements.

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“…If only real entries of the perturbation matrices δM, δC and δK are allowed, then the corresponding real stability radius can be calculated following [21] and [13] as…”

Section: Real Stability Radiusmentioning

confidence: 99%

“…An overview on pseudospectra and robust stability analysis for timedelay systems can be found in [20]. Real stability radius for time-delay systems was introduced in [21] and in [13]. The formulas for unstructured and weighted structured complex stability radii for time-delay systems were given in [19] and [35], respectively.…”

mentioning

confidence: 99%

Robust stability analysis of machining operations

Hajdu

Insperger

Stépàn

2016

Int J Adv Manuf Technol

View full text Add to dashboard Cite

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“…The decision on robust stability can be made by using robust stability indices (Hu and Davison, 2003). Assume that the perturbed system (20) can be written in the form:…”

Section: Stability Radius and Robust Stabilitymentioning

confidence: 99%

“…Provided that the unperturbed system (20) is stable, the real structured stability radius of Equation 23 is defined as (Hu and Davison, 2003):…”

Section: Stability Radius and Robust Stabilitymentioning

confidence: 99%

“…The real stability radius problem concerns the computation of the real stability radius when the nominal system is known. The stability radius is computed by using the method presented in (Hu and Davison, 2003). The obtained stability radius provides a basis for assigning eigenvalues for robust stability of systems of DDEs with uncertain parameters.…”

Section: Stability Radius and Robust Stabilitymentioning

confidence: 99%

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Analysis of Time-Delayed Neural Networks via Rightmost Eigenvalue Positions

Yi¹,

Yu²,

Kim³

et al. 2015

American Journal of Engineering and Applied Sciences

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Neural networks have been frequently used in various areas. In the implementation of the networks, time delays and uncertainty are present and known to lead to complex behaviors, which are hard to predict using classical analysis methods. In this study, stability and robust stability of neural networks considering time delays and parametric uncertainty is studied. For stability analysis, the rightmost eigenvalues (or dominant characteristic roots) are obtained by using an approach based on the Lambert W function. The Lambert W function has already been embedded in various commercial software packages (e.g., MATLAB, Maple and Mathematica). In a way similar to non-delayed systems, stability is determined from the positions of the characteristic roots in the complex plane. Conditions for oscillation and robust stability are also given. Numerical examples are provided and the results are compared to existing approaches (e.g., bifurcation method) and discussed.

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Strong stability radii of positive linear time-delay systems

Ngoc¹

2005

Int. J. Robust Nonlinear Control

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SUMMARYIn this paper, we study robustness of the strong delay-independent stability of linear time-delay systems under multi-perturbation and affine perturbation of coefficient matrices via the concept of strong delayindependent stability radius (shortly, strong stability radius). We prove that for class of positive time-delay systems, complex and real strong stability radii of positive linear time-delay systems under multiperturbations (or affine perturbations) coincide and they are computed via simple formulae. Apart from that, we derive solution of a global optimization problem associated with the problem of computing of the strong stability radii of a positive linear time-delay system. An example is given to illustrate the obtained results.

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Real stability radii of linear time-invariant time-delay systems

Cited by 31 publications

References 17 publications

Robust stability analysis of machining operations

Robust stability analysis of machining operations

Analysis of Time-Delayed Neural Networks via Rightmost Eigenvalue Positions

Strong stability radii of positive linear time-delay systems

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