Relative Controllability of Nonlinear Fractional Damped Delay Systems with Multiple Delays in Control

2020 ◽  
pp. 367-378 ◽  
Author(s):  
P. Suresh Kumar
Keyword(s):  
Delay Systems ◽  
Multiple Delays ◽  
Relative Controllability

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 Relative controllability of multiagent systems with pairwise different delays in states

2022 ◽  
Vol 27 ◽  
pp. 1-19
Author(s):  
Yuanchao Si ◽  
JinRong Wang
Keyword(s):  
Differential Equation ◽  
Multiagent Systems ◽  
Delay System ◽  
Multiple Delays ◽  
Information Flows ◽  
Relative Controllability ◽  
Delay Differential ◽  
Time Invariant ◽  
Interaction Topology ◽  
Generic Time

In this manuscript, relative controllability of leader–follower multiagent systems with pairwise different delays in states and fixed interaction topology is considered. The interaction topology of the group of agents is modeled by a directed graph. The agents with unidirectional information flows are selected as leaders, and the others are followers. Dynamics of each follower obeys a generic time-invariant delay differential equation, and the delays of agents, which satisfy a specified condition, are different one another because of the degeneration or burn-in of sensors. With a neighbor-based protocol steering, the dynamics of followers become a compact form with multiple delays. Solution of the multidelayed system without pairwise matrices permutation is obtained by improving the method in the references, and relative controllability is established via Gramian criterion. Further rank criterion of a single delay system is dealt with. Simulation illustrates the theoretical deduction.

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.

Robust Controller Design for Discrete Uncertain Multiple Time-Delay Systems

1997 ◽  
Vol 119 (1) ◽  
pp. 122-127 ◽  
Author(s):  
Feng-Hsiag Hsiao ◽  
Shing-Tai Pan ◽  
Ching-Cheng Teng
Keyword(s):  
Time Delay ◽  
Uncertain Systems ◽  
Controller Design ◽  
Delay Systems ◽  
Multiple Delays ◽  
Multiple Time ◽  
Time Delay Systems ◽  
Ultimate Boundedness ◽  
Robust Controller ◽  
Robust Controller Design

We derive a variety of succinct criteria of robust stability for discrete uncertain systems which contain multiple delays and a class of series nonlinearities. Each result is expressed by a brief inequality and corresponds to compromise between simplicity and sharpness. The properties of norm are employed to investigate robustness conditions that guarantee asymptotic stability rather than ultimate boundedness of trajectories. It is shown that the uncertainties, nonlinearities, and delays are the factors of instability of the overall system, between which some compromise is necessary.

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