Robust Stability Conditions Based on Eigenstructure Assignment for Uncertain Time-Delay Systems: The Continuous-Time Case

1996 ◽  
Vol 29 (1) ◽  
pp. 3526-3531
Author(s):  
Hansheng Wu ◽  
Koichi Mizukami
Keyword(s):  
Time Delay ◽  
Robust Stability ◽  
Continuous Time ◽  
Delay Systems ◽  
Stability Conditions ◽  
Eigenstructure Assignment ◽  
Time Delay Systems ◽  
Uncertain Time

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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