A practical method for analyzing the stability of neutral type LTI-time delayed systems

Automatica ◽  
2004 ◽  
Vol 40 (5) ◽  
pp. 847-853 ◽  
Author(s):  
Nejat Olgac ◽  
Rifat Sipahi
Keyword(s):  
Neutral Type ◽  
Practical Method ◽  
Delayed Systems ◽  
The Stability

The Cluster Treatment of Characteristic Roots and the Neutral Type Time-Delayed Systems

2004 ◽  
Author(s):  
Nejat Olgac ◽  
Rifat Sipahi
Keyword(s):  
Time Delay ◽  
Linear Time ◽  
Neutral Type ◽  
Direct Consequence ◽  
Necessary Condition ◽  
Delayed Systems ◽  
Linear Time Invariant ◽  
Characteristic Roots ◽  
Stability Intervals ◽  
The Stability

A new methodology is presented for assessing the stability posture of a general class of linear time-invariant – neutral time-delayed systems (LTI-NTDS). It is based on a “Cluster Treatment of Characteristic Roots CTCR” paradigm. The technique offers a number of unique features: It returns exact bounds of time delay for stability, furthermore it yields the number of unstable characteristic roots of the system in an explicit and non-sequentially evaluated function of time delay. As a direct consequence of the latter feature, the new methodology creates entirely, all existing stability intervals of delay, τ. It is shown that the CTCR inherently enforces an intriguing necessary condition for τ-stabilizability, which is the main contribution of this paper. This, so called “small delay” effect, was recognized earlier for NTDS, only through some cumbersome mathematics. In addition to the above listed characteristics, the CTCR is also unique in handling systems with unstable starting posture for τ = 0, which may be τ-stabilized for higher values of delay. Example cases are provided.

Direct method for analyzing the stability of neutral type LTI-time delayed systems

2003 ◽  
Vol 36 (19) ◽  
pp. 29-34 ◽  
Author(s):  
Nejat Olgac ◽  
Rifat Sipahi
Keyword(s):  
Direct Method ◽  
Neutral Type ◽  
Delayed Systems ◽  
The Stability

Seismic stability analyses of reinforced tapered landfill cover systems considering seepage forces

2018 ◽  
Vol 36 (4) ◽  
pp. 361-372 ◽  
Author(s):  
Afshin Khoshand ◽  
Ali Fathi ◽  
Milad Zoghi ◽  
Hamidreza Kamalan
Keyword(s):  
Parametric Study ◽  
Limit Equilibrium ◽  
Practical Method ◽  
Seismic Stability ◽  
Design Parameters ◽  
Cover System ◽  
Landfill Cover ◽  
Cover Systems ◽  
Landfill Cover System ◽  
The Stability

One of the most common and economical methods for waste disposal is landfilling. The landfill cover system is one of the main components of landfills which prevents waste exposure to the environment by creating a barrier between the waste and the surrounding environment. The stability and integrity of the landfill cover system is a fundamental part of the design, construction, and maintenance of landfills. A reinforced tapered landfill cover system can be considered as a practical method for improving its stability; however, the simultaneous effects of seismic and seepage forces in the reinforced tapered landfill cover system have not been studied. The current paper provides a solution based on the limit equilibrium method in order to evaluate the stability of a reinforced tapered landfill cover system under seismic and seepage (both horizontal and parallel seepage force patterns) loading conditions. The proposed analytical approach is applied to different design cases through parametric study and the obtained results are compared to those derived from literature. Parametric study is performed to illustrate the sensitivity of the safety factor (FS) to the different design parameters. The obtained results reveal that parameters which describe the geometry have limited effects on the stability of the landfill cover system in comparison to the rest of the studied design parameters. Moreover, the comparisons between the derived results and available methods demonstrate good agreement between obtained findings with those reported in the literature.

Kernel and Offspring Concepts for the Stability Robustness of Multiple Time Delayed Systems (MTDS)

2006 ◽  
Vol 129 (3) ◽  
pp. 245-251 ◽  
Author(s):  
Rifat Sipahi ◽  
Nejat Olgac
Keyword(s):  
Time Delays ◽  
Linear Time ◽  
Characteristic Root ◽  
Invariance Property ◽  
Multiple Time ◽  
Delayed Systems ◽  
Linear Time Invariant ◽  
Characteristic Roots ◽  
Stability Robustness ◽  
The Stability

A novel treatment for the stability of linear time invariant (LTI) systems with rationally independent multiple time delays is presented in this paper. The independence of delays makes the problem much more challenging compared to systems with commensurate time delays (where the delays have rational relations). We uncover some wonderful features for such systems. For instance, all the imaginary characteristic roots of these systems can be found exhaustively along a set of surfaces in the domain of the delays. They are called the “kernel” surfaces (curves for two-delay cases), and it is proven that the number of the kernel surfaces is manageably small and bounded. All possible time delay combinations, which yield an imaginary characteristic root, lie either on this kernel or its infinitely many “offspring” surfaces. Another hidden feature is that the root tendencies along these surfaces exhibit an invariance property. From these outstanding characteristics an efficient, exact, and exhaustive methodology results for the stability assessment. As an added uniqueness of this method, the systems under consideration do not have to be stable for zero delays. Several example case studies are presented, which are prohibitively difficult, if not impossible to solve using any other peer methodology known to the authors.

On the stability of nonlinear systems of the neutral type

1975 ◽  
Vol 39 (1) ◽  
pp. 38-45 ◽  
Author(s):  
V.P. Skripnik
Keyword(s):  
Nonlinear Systems ◽  
Neutral Type ◽  
The Stability

An Improved Delay-Dependent Stability Criterion for a Class of Lur’e Systems of Neutral Type

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
K. Ramakrishnan ◽  
G. Ray
Keyword(s):  
Stability Analysis ◽  
Stability Criterion ◽  
Time Derivative ◽  
Neutral Type ◽  
Linear Matrix ◽  
Lur’E Systems ◽  
The Stability ◽  
Delay Dependent ◽  
Bounded Nonlinearity ◽  
Delay Dependent Stability

In this paper, we consider the problem of delay-dependent stability of a class of Lur’e systems of neutral type with time-varying delays and sector-bounded nonlinearity using Lyapunov–Krasovskii (LK) functional approach. By using a candidate LK functional in the stability analysis, a less conservative absolute stability criterion is derived in terms of linear matrix inequalities (LMIs). In addition to the LK functional, conservatism in the proposed stability analysis is further reduced by imposing tighter bounding on the time-derivative of the functional without neglecting any useful terms using minimal number of slack matrix variables. The proposed analysis, subsequently, yields a stability criterion in convex LMI framework, and is solved nonconservatively at boundary conditions using standard LMI solvers. The effectiveness of the proposed criterion is demonstrated through a standard numerical example and Chua’s circuit.

scholarly journals Effect of Leakage Delay on Stability of Neutral-Type Genetic Regulatory Networks

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Li Li ◽  
Yongqing Yang ◽  
Chuanzhi Bai
Keyword(s):  
Regulatory Network ◽  
Regulatory Networks ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Genetic Regulatory Networks ◽  
Genetic Regulatory Network ◽  
Leakage Delay ◽  
Leakage Delays ◽  
The Stability

The stability of neutral-type genetic regulatory networks with leakage delays is considered. Firstly, we describe the model of genetic regulatory network with neutral delays and leakage delays. Then some sufficient conditions are derived to ensure the asymptotic stability of the genetic regulatory network by the Lyapunov functional method. Further, the effect of leakage delay on stability is discussed. Finally, a numerical example is given to show the effectiveness of the results.

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.

scholarly journals Necessary and Sufficient Conditions For The Stability Of Uncertain Input-Delayed Systems

2018 ◽  
Vol 51 (14) ◽  
pp. 218-223
Author(s):  
Berna Bou Farraa ◽  
Rosa Abbou ◽  
Jean Jacques Loiseau
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Delayed Systems ◽  
Uncertain Input ◽  
The Stability ◽  
Necessary And Sufficient
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