scholarly journals Stability analysis and observer design for a class of nonlinear systems with multiple time-delays

2013 ◽  
Vol 2013 (1) ◽  
Author(s):  
Yali Dong ◽  
Fengwei Yang
Keyword(s):  
Stability Analysis ◽  
Nonlinear Systems ◽  
Time Delays ◽  
Observer Design ◽  
Multiple Time ◽  
Multiple Time Delays

Stability Analysis of Multiple Time Delayed Systems Using the Direct Method

2003 ◽  
Author(s):  
Rifat Sipahi ◽  
Nejat Olgac
Keyword(s):  
Stability Analysis ◽  
Time Delays ◽  
Linear Time ◽  
Direct Method ◽  
Multiple Time ◽  
Delayed Systems ◽  
Practical Applications ◽  
Linear Time Invariant ◽  
Multiple Time Delays ◽  
The Stability

A novel treatment for the stability of a class of linear time invariant (LTI) systems with rationally independent multiple time delays using the Direct Method (DM) is studied. Since they appear in many practical applications in the systems and control community, this class of dynamics has attracted considerable interest. The stability analysis is very complex because of the infinite dimensional nature (even for single delay) of the dynamics and furthermore the multiplicity of these delays. The stability problem is much more challenging compared to the TDS with commensurate time delays (where time delays have rational relations). It is shown in an earlier publication of the authors that the DM brings a unique, exact and structured methodology for the stability analysis of commensurate time delayed cases. The transition from the commensurate time delays to multiple delay case motivates our study. It is shown that the DM reveals all possible stability regions in the space of multiple time delays. The systems that are considered do not have to possess stable behavior for zero delays. We present a numerical example on a system, which is considered “prohibitively difficult” in the literature, just to exhibit the strengths of the new procedure.

Delay-independent stabilization of nonlinear systems with multiple time-delays and its application in chaos synchronization of Rössler system

2016 ◽  
Vol 9 (2) ◽  
pp. 205-216 ◽  
Author(s):  
Ping He ◽  
Tao Fan
Keyword(s):  
Nonlinear Systems ◽  
Time Delays ◽  
Chaos Synchronization ◽  
Linear Matrix ◽  
Multiple Time ◽  
Content Type ◽  
Multiple Time Delays ◽  
Rossler System ◽  
Rössler System ◽  
And Algebra

Purpose – The purpose of this paper is with delay-independent stabilization of nonlinear systems with multiple time-delays and its application in chaos synchronization of Rössler system. Design/methodology/approach – Based on linear matrix inequality and algebra Riccati matrix equation, the stabilization result is derived to guarantee asymptotically stable and applicated in chaos synchronization of Rössler chaotic system with multiple time-delays. Findings – A controller is designed and added to the nonlinear system with multiple time-delays. The stability of the nonlinear system at its zero equilibrium point is guaranteed by applying the appropriate controller signal based on linear matrix inequality and algebra Riccati matrix equation scheme. Another effective controller is also designed for the global asymptotic synchronization on the Rössler system based on the structure of delay-independent stabilization of nonlinear systems with multiple time-delays. Numerical simulations are demonstrated to verify the effectiveness of the proposed controller scheme. Originality/value – The introduced approach is interesting for delay-independent stabilization of nonlinear systems with multiple time-delays and its application in chaos synchronization of Rössler system.

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