scholarly journals Stability analysis of linear neutral systems with multiple time delays

2005 ◽  
Vol 2005 (2) ◽  
pp. 175-183 ◽  
Author(s):  
Keyue Zhang
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Spectral Radius ◽  
Time Delays ◽  
Multiple Time ◽  
Stability Criteria ◽  
Neutral Systems ◽  
Numerical Examples ◽  
Multiple Time Delays ◽  
New Criteria

This paper studies the asymptotic stability of linear neutral systems with multiple time delays. Using the characteristic equation of the system, new delay-independent stability criteria are derived in terms of the spectral radius of modulus matrices. Numerical examples are given to demonstrate the validity of our new criteria.

Discrete-Delay-Independent and Discrete-Delay-Dependent Criteria for a Class of Neutral Systems

2003 ◽  
Vol 125 (1) ◽  
pp. 33-41 ◽  
Author(s):  
Chang-Hua Lien ◽  
Jenq-Der Chen
Keyword(s):  
Time Delays ◽  
Linear Matrix ◽  
Multiple Time ◽  
Matrix Inequality ◽  
Stability Criteria ◽  
Discrete Delay ◽  
Neutral Systems ◽  
Numerical Examples ◽  
Multiple Time Delays ◽  
Delay Dependent

In this paper, the asymptotic stability for a class of neutral systems with discrete and distributed multiple time delays is considered. Discrete-delay-independent and discrete-delay-dependent criteria are proposed to guarantee stability for such systems. The resulting stability criteria are written in the form of spectral radius and linear matrix inequality (LMI). Some numerical examples are given to illustrate that our obtained results are less conservative.

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.

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