scholarly journals Some special cases in the stability analysis of multi-dimensional time-delay systems using the matrix Lambert W function

Automatica ◽  
2015 ◽  
Vol 53 ◽  
pp. 339-345 ◽  
Author(s):  
Rudy Cepeda-Gomez ◽  
Wim Michiels
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Delay Systems ◽  
Lambert W Function ◽  
Time Delay Systems ◽  
Special Cases ◽  
The Matrix ◽  
The Stability

scholarly journals Analysis of Multidimensional Time Delay Systems Using Lambert W Function

2017 ◽  
Vol 139 (11) ◽  
Author(s):  
Niraj Choudhary ◽  
Janardhanan Sivaramakrishnan ◽  
Indra Narayan Kar
Keyword(s):  
Time Delay ◽  
Delay System ◽  
Nyquist Plot ◽  
Delay Systems ◽  
Lambert W Function ◽  
Order System ◽  
Complex Conjugate ◽  
Time Delay Systems ◽  
Special Cases ◽  
The Matrix

In this note, the analysis of time delay systems (TDSs) using Lambert W function approach is reassessed. A common canonical (CC) form of time delay systems is defined. We extended the recent results of Cepeda–Gomez and Michiels (2015, “Some Special Cases in the Stability Analysis of Multi-Dimensional Time-Delay Systems Using the Matrix Lambert W Function,” Automatica, 53, pp. 339–345) for second-order into nth order system. The eigenvalues of a time delay system are either real or complex conjugate pairs and therefore, the whole eigenspectrum can be associated with only two real branches of the Lambert W function. A new class of time delay systems is characterized to extend the applicability of the above-said method. Moreover, this approach has been exploited to design a controller which places a subset of eigenvalues at desired locations. Stability is guaranteed by using a new algorithm developed in this paper, which is based on the Nyquist plot. The approach is validated through numerical examples.

scholarly journals New model transformations for the stability analysis of time-delay systems

2018 ◽  
Vol 51 (14) ◽  
pp. 124-129
Author(s):  
Mohammed Safi ◽  
Lucie Baudouin ◽  
Alexandre Seuret
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Delay Systems ◽  
Model Transformations ◽  
Time Delay Systems ◽  
New Model ◽  
The Stability

On Stability Analysis of Switched Linear Time-Delay Systems under Arbitrary Switching

2015 ◽  
pp. 480-515 ◽  
Author(s):  
Marwen Kermani ◽  
Anis Sakly
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Lyapunov Function ◽  
Continuous Time ◽  
Delay System ◽  
Delay Systems ◽  
Stability Conditions ◽  
Time Delay Systems ◽  
Arbitrary Switching ◽  
The Stability

This chapter focuses on the stability analysis problem for a class of continuous-time switched time-delay systems modelled by delay differential equations under arbitrary switching. Then, a transformation under the arrow form is employed. Indeed, by using a constructed Lyapunov function, the aggregation techniques, the Kotelyanski lemma associated with the M-matrix properties, new delay-dependent sufficient stability conditions are derived. The obtained results provide a solution to one of the basic problems in continuous-time switched time-delay systems. This problem ensures asymptotic stability of the switched time-delay system under arbitrary switching signals. In addition, these stability conditions are extended to be generalized for switched systems with multiple delays. Noted that, these obtained results are explicit, simple to use, and allow us to avoid the problem of searching a common Lyapunov function. Finally, two examples are provided, with numerical simulations, to demonstrate the effectiveness of the proposed method.

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