Spectrum-Based Robust Stability Analysis of Linear Delay Differential-Algebraic Equations

2015 ◽  
pp. 533-557 ◽  
Author(s):  
Vu Hoang Linh ◽  
Do Duc Thuan
Keyword(s):  
Stability Analysis ◽  
Robust Stability ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Robust Stability Analysis ◽  
Linear Delay ◽  
Delay Differential

scholarly journals On the Stability Analysis of Delay Differential-Algebraic Equations

2018 ◽  
Vol 34 (2) ◽  
Author(s):  
Phi Ha
Keyword(s):  
Stability Analysis ◽  
Exponential Stability ◽  
Linear Time ◽  
Differential Algebraic Equations ◽  
Spectral Condition ◽  
Algebraic Equations ◽  
Linear Time Invariant ◽  
Stability Of Dynamical Systems ◽  
The Stability ◽  
Delay Differential

The stability analysis of linear time invariant delay differentialalgebraic equations (DDAEs) is analyzed. Examples are delivered to demonstrate that the eigenvalue-based approach to analyze the exponential stability of dynamical systems is not valid for an arbitrarily high index system, and hence, a new concept of weakly exponential stability (w.e.s) is proposed. Then, we characterize the w.e.s in term of a spectral condition for some special classes of DDAEs.

scholarly journals Discontinuity Propagation in Delay Differential-Algebraic Equations

2018 ◽  
Vol 34 ◽  
pp. 582-601 ◽  
Author(s):  
Benjamin Unger
Keyword(s):  
Differential Algebraic Equations ◽  
Complete Characterization ◽  
Algebraic Equations ◽  
Case Scenario ◽  
Worst Case ◽  
Linear Delay ◽  
Method Of Steps ◽  
Matrix Pencils ◽  
Delay Differential ◽  
The Impact

The propagation of primary discontinuities in initial value problems for linear delay differential-algebraic equations (DDAEs) is discussed. Based on the (quasi-) Weierstra{\ss} form for regular matrix pencils, a complete characterization of the different propagation types is given and algebraic criteria in terms of the matrices are developed. The analysis, which is based on the method of steps, takes into account all possible inhomogeneities and history functions and thus serves as a worst-case scenario. Moreover, it reveals possible hidden delays in the DDAE and allows to study exponential stability of the DDAE based on the spectral abscissa. The new classification for DDAEs is compared to existing approaches in the literature and the impact of splicing conditions on the classification is studied.

Computation and Stability Analysis of Solutions of Periodic Delay Differential Algebraic Equations

2005 ◽  
Author(s):  
Koen Verheyden ◽  
Kurt Lust ◽  
Dirk Roose
Keyword(s):  
Stability Analysis ◽  
Numerical Methods ◽  
Periodic Solutions ◽  
Numerical Algorithms ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Periodic Delay ◽  
Delay Differential ◽  
Time Periodic ◽  
Periodic Delays

This paper is concerned with the numerical computation, continuation and stability analysis of periodic solutions of periodic delay differential algebraic equations. We consider systems with a time-periodic right hand side function and time-periodic delays. We introduce numerical algorithms based on collocation to compute periodic solutions and their stability. The presented methods combine knowledge from numerical methods for delay equations and differential algebraic equations. Our algorithms are illustrated with numerical results for two models.

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