Stability conditions for linear continuous time difference systems with discrete and distributed delay

2011 ◽  
Author(s):  
Daniel Melchor-Aguilar
Keyword(s):  
Continuous Time ◽  
Distributed Delay ◽  
Time Difference ◽  
Stability Conditions ◽  
Difference Systems

scholarly journals Estimates for the norms of solutions of delay difference systems

2002 ◽  
Vol 30 (11) ◽  
pp. 697-703 ◽  
Author(s):  
Rigoberto Medina
Keyword(s):  
Difference Equations ◽  
Stability Conditions ◽  
Partial Difference Equations ◽  
Partial Difference ◽  
Difference Systems ◽  
Reaction Processes ◽  
Delay Difference Equations ◽  
Model Diffusion ◽  
Delay Difference

We derive explicit stability conditions for delay difference equations inℂn(the set ofncomplex vectors) and estimates for the size of the solutions are derived. Applications to partial difference equations, which model diffusion and reaction processes, are given.

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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