Complete type Lyapunov functionals for integral delay systems with multiple delays

2021 ◽  
Author(s):  
Daniel Melchor‐Aguilar ◽  
Hector Arismendi‐Valle
Keyword(s):  
Delay Systems ◽  
Multiple Delays ◽  
Lyapunov Functionals ◽  
Complete Type

Equivalency of Stability Transitions Between the SDS (Spectral Delay Space) and DS (Delay Space)

2013 ◽  
Author(s):  
Qingbin Gao ◽  
Umut Zalluhoglu ◽  
Nejat Olgac
Keyword(s):  
Linear Time ◽  
Broad Class ◽  
Delay Systems ◽  
Multiple Delays ◽  
Delayed Systems ◽  
Linear Time Invariant ◽  
Time In Literature ◽  
The Stability ◽  
Time Invariant ◽  
Delay Space

It has been shown that the stability of LTI time-delayed systems with respect to the delays can be analyzed in two equivalent domains: (i) delay space (DS) and (ii) spectral delay space (SDS). Considering a broad class of linear time-invariant time delay systems with multiple delays, the equivalency of the stability transitions along the transition boundaries is studied in both spaces. For this we follow two corresponding radial lines in DS and SDS, and prove for the first time in literature that they are equivalent. This property enables us to extract local stability transition features within the SDS without going back to the DS. The main advantage of remaining in SDS is that, one can avoid a non-linear transition from kernel hypercurves to offspring hypercurves in DS. Instead the potential stability switching curves in SDS are generated simply by stacking a finite dimensional cube called the building block (BB) along the axes. A case study is presented within the report to visualize this property.

scholarly journals Full and Reduced-Order Unknown Input Observer Design for Linear Time-Delay Systems with Multiple Delays

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Seifeddine Ben Warrad ◽  
Olfa Boubaker ◽  
Mihai Lungu ◽  
Saleh Mobayen
Keyword(s):  
Time Delay ◽  
Linear Time ◽  
Observer Design ◽  
Delay Systems ◽  
Multiple Delays ◽  
Unknown Input ◽  
Time Delay Systems ◽  
Reduced Order ◽  
Unknown Input Observers ◽  
Existence Conditions

In this work, we consider the design problem of a full-order and also reduced-order unknown input observers for a particular class of time-delay systems. Asymptotic stability and existence conditions for the designed observers are established. The quadruple-tank process is used as a benchmark to prove the efficiency of the proposed algorithms.

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