scholarly journals Characteristic equation approach to stability measures of linear neutral systems with multiple time delays

2007 ◽  
Vol 17 (1) ◽  
pp. 95-105
Author(s):  
D. Q. Cao ◽  
◽  
Y. R. Yang ◽  
Y. M. Ge ◽  
Keyword(s):  
Characteristic Equation ◽  
Time Delays ◽  
Multiple Time ◽  
Equation Approach ◽  
Neutral Systems ◽  
Multiple Time Delays

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.

Stability analysis of connected vehicles with V2V communication and time delays: CTCR method via Bézout’s resultant

2021 ◽  
pp. 014233122098142
Author(s):  
Sirin Akkaya ◽  
Onur Akbati ◽  
Ali Fuat Ergenc
Keyword(s):  
Characteristic Equation ◽  
Time Delays ◽  
Characteristic Root ◽  
Sufficient Conditions ◽  
Connected Vehicles ◽  
Multiple Time ◽  
String Stability ◽  
V2v Communication ◽  
Multiple Time Delays ◽  
Input Delays

This paper is focused on the distributed control of connected vehicles via vehicle-to-vehicle (V2V) communication. A mixed predecessor following topology with a virtual leader under constant time headway policy is analysed in case of communication and input delays. The longitudinal dynamics of each vehicle in the platoon is represented by a third-order linear model. Unavoidable communication and input delays are introduced into the platoon structure which converts the characteristic equation of the system into a transcendental type. The stability regions of the system in delay space are obtained by utilizing the cluster treatment of characteristic root (CTCR) method in the case of single and multiple time delays. A new Bézout resultant matrix-based approach is proposed to determine the kernel and offspring hypersurfaces of the CTCR method. The determination of these kernel and offspring hypersurfaces becomes computational costly as the number of vehicles increases in the platoon due to the increasing degree of characteristic equation. However, the proposed method reduces the dimensions of the coefficient matrix which is created by using the characteristic equation. It is concluded that the proposed method confirms the internal stability of the connected vehicles with both generic information flow topologies and formation between vehicles under single and multiple time delays. Thereafter, a local string stability definition is proposed in terms of spacing errors. Sufficient conditions to obtain string stability under mixed predecessor following topology for the existence and nonexistence of time delay are given. Finally, several simulation studies with different scenarios are conducted to display the effectiveness of the proposed model and method for internal and string stabilities.

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.

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