The principle of the argument and its application to the stability and robust stability problems

2007 ◽  
pp. 16-23
Author(s):  
Mohamed Mansour
Keyword(s):  
Robust Stability ◽  
Stability Problems ◽  
The Stability

scholarly journals Stability Analysis of Distributed Order Fractional Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
H. Saberi Najafi ◽  
A. Refahi Sheikhani ◽  
A. Ansari
Keyword(s):  
Stability Analysis ◽  
Characteristic Function ◽  
Differential Equations ◽  
Density Function ◽  
Robust Stability ◽  
Fractional Differential Equations ◽  
Stability Condition ◽  
Fractional Differential ◽  
The Stability ◽  
Distributed Order

We analyze the stability of three classes of distributed order fractional differential equations (DOFDEs) with respect to the nonnegative density function. In this sense, we discover a robust stability condition for these systems based on characteristic function and new inertia concept of a matrix with respect to the density function. Moreover, we check the stability of a distributed order fractional WINDMI system to illustrate the validity of proposed procedure.

scholarly journals Global Exponential Robust Stability of Static Interval Neural Networks with Time Delay in the Leakage Term

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Guiying Chen ◽  
Linshan Wang
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Robust Stability ◽  
Sufficient Conditions ◽  
Leakage Term ◽  
Interval Neural Networks ◽  
Global Exponential Robust Stability ◽  
The Stability ◽  
Delay Differential ◽  
Delay Differential Inequality

The stability of a class of static interval neural networks with time delay in the leakage term is investigated. By using the method ofM-matrix and the technique of delay differential inequality, we obtain some sufficient conditions ensuring the global exponential robust stability of the networks. The results in this paper extend the corresponding conclusions without leakage delay. An example is given to illustrate the effectiveness of the obtained results.

Optimization of the Robust Stability Limit for Multi-Cutter Turning Processes

2015 ◽  
Author(s):  
Marta J. Reith ◽  
Daniel Bachrathy ◽  
Gabor Stepan
Keyword(s):  
Robust Stability ◽  
Optimal Parameter ◽  
Stability Limit ◽  
Boundary Function ◽  
Lower Envelope ◽  
Computation Method ◽  
Parameter Region ◽  
Dynamical Parameters ◽  
The Stability ◽  
Machining Parameter

Multi-cutter turning systems bear huge potential in increasing cutting performance. In this study we show that the stable parameter region can be extended by the optimal tuning of system parameters. The optimal parameter regions can be identified by means of stability charts. Since the stability boundaries are highly sensitive to the dynamical parameters of the machine tool, the reliable exploitation of the so-called stability pockets is limited. Still, the lower envelope of the stability lobes is an appropriate upper boundary function for optimization purposes with an objective function taken for maximal material removal rates. This lower envelope is computed by the Robust Stability Computation method presented in the paper. It is shown in this study, that according to theoretical results obtained for optimally tuned cutters, the safe stable machining parameter region can significantly be extended, which has also been validated by machining tests.

A New, Necessary and Sufficient Vertex Solution for Robust Stability Check of Unstructured Convex Combination Matrix Families

2015 ◽  
Author(s):  
Rama K. Yedavalli
Keyword(s):  
Robust Stability ◽  
Convex Combination ◽  
Convexity Property ◽  
Ecological Principles ◽  
Sign Structure ◽  
Previous Solution ◽  
Peer Community ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Complete Dependence

This paper revisits the problem of checking the robust stability of matrix families generated by ‘Unstructured Convex Combinations’ of user supplied or externally supplied Vertex Matrices. A previous solution given by the author for this problem involved complete dependence on the quantitative (eigenvalue information) of a set of special matrices labeled the Kronecker Nonsingularity (KN) matrices. In this solution, the ‘convexity’ property is not explicit and transparent, to the extent that, unfortunately, the accuracy of the solution itself is being questioned and not embraced by the peer community. To erase this unforunate and unwarranted image of this author (in this specific problem) in the minds of the peer community, in this paper, the author treads a new path to find a solution that brings out the convexity property in an explicit and understandable way. In the new solution presented in this paper, we combine the qualitative (sign) as well as quantitative (magnitude) information of these KN matrices and present a vertex solution in which the convexity property of the solution is transparent making it more elegant and accepatble to the peer community, than the previous solution. The new solution clearly underscores the importance of using the sign structure of a matrix in assessing the stability of a matrix. This new solution is made possible by the new insight provided by the qualitative (sign) stability/instability derived from ecological principles. Examples are given which clearly demonstrate effectiveness of the new, convexity based algorithm. It is hoped that this new solution will be embraced by the peer community.

scholarly journals A General Theorem on the Stability of a Class of Functional Equations Including Quartic-Cubic-Quadratic-Additive Equations

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 282
Author(s):  
Yang-Hi Lee ◽  
Soon-Mo Jung
Keyword(s):  
Functional Equations ◽  
Direct Method ◽  
General Theorem ◽  
Stability Problems ◽  
General Stability ◽  
Stability Theorems ◽  
Additive Type ◽  
The Stability

We prove general stability theorems for n-dimensional quartic-cubic-quadratic-additive type functional equations of the form by applying the direct method. These stability theorems can save us the trouble of proving the stability of relevant solutions repeatedly appearing in the stability problems for various functional equations.

scholarly journals A Panoramic Sketch about the Robust Stability of Time-Delay Systems and Its Applications

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-26
Author(s):  
Baltazar Aguirre-Hernández ◽  
Raúl Villafuerte-Segura ◽  
Alberto Luviano-Juárez ◽  
Carlos Arturo Loredo-Villalobos ◽  
Edgar Cristian Díaz-González
Keyword(s):  
Time Delay ◽  
Dynamical Systems ◽  
Robust Stability ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Complex Dynamical Systems ◽  
The Stability ◽  
Numerical Approaches

This paper presents a brief review on the current applications and perspectives on the stability of complex dynamical systems, with an emphasis on three main classes of systems such as delay-free systems, time-delay systems, and systems with uncertainties in its parameters, which lead to some criteria with necessary and/or sufficient conditions to determine stability and/or stabilization in the domains of frequency and time. Besides, criteria on robust stability and stability of nonlinear time-delay systems are presented, including some numerical approaches.

scholarly journals Low Conservative Criteria for Robust Consensus of Multiagent Systems with Delays, Disturbances, and Topologies Uncertainties

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Qingjie Zhang ◽  
Zhongqing Jin ◽  
Qiang Li ◽  
Jianwu Tao ◽  
Qiongjian Fan ◽  
...  
Keyword(s):  
Multiagent Systems ◽  
Robust Stability ◽  
Linear Matrix ◽  
Multiple Time ◽  
Matrix Inequality ◽  
Space Transformation ◽  
Strongly Connected ◽  
Nonlinear Matrix Inequality ◽  
The Stability ◽  
Robust Consensus

Considering the limited communications conditions such as delays, disturbances, and topologies uncertainties, the stability criteria for robust consensus of multiagent systems are proposed in this paper. Firstly, by using the idea of state decomposition and space transformation, the condition for guaranteeing consensus is converted into verifying the robust stability of the disagreement system. In order to deal with multiple time-varying delays and switching topologies, jointly quadratic common Lyapunov-Krasovskii (JQCLK) functional is built to analyze the robust stability. Then, the numerical criterion can be obtained through solving the corresponding feasible nonlinear matrix inequality (NLMI); at last, nonlinear minimization is used like solving cone complementarity problem. Therefore, the linear matrix inequality (LMI) criterion is obtained, which can be solved by mathematical toolbox conveniently. In order to relax the conservativeness, free-weighting matrices (FWM) method is employed. Further, the conclusion is extended to the case of strongly connected topologies. Numerical examples and simulation results are given to demonstrate the effectiveness and the benefit on reducing conservativeness of the proposed criteria.

scholarly journals Analysis of Robust Stability for a Class of Stochastic Systems via Output Feedback: The LMI Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Xin-rong Cong ◽  
Long-suo Li
Keyword(s):  
Linear Matrix Inequality ◽  
Robust Stability ◽  
Output Feedback ◽  
Stochastic Systems ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Convex Optimization Problem ◽  
Control Laws ◽  
The Stability ◽  
And Control

This paper investigates the robust stability for a class of stochastic systems with both state and control inputs. The problem of the robust stability is solved via static output feedback, and we convert the problem to a constrained convex optimization problem involving linear matrix inequality (LMI). We show how the proposed linear matrix inequality framework can be used to select a quadratic Lyapunov function. The control laws can be produced by assuming the stability of the systems. We verify that all controllers can robustly stabilize the corresponding system. Further, the numerical simulation results verify the theoretical analysis results.

Robust Stability Analysis of “Unstructured” Convex Combinations of Matrices With Applications

2006 ◽  
Author(s):  
Rama K. Yedavalli
Keyword(s):  
Stability Analysis ◽  
Robust Stability ◽  
Convex Combination ◽  
Problem Formulation ◽  
Solution Algorithms ◽  
Robust Stability Analysis ◽  
Problem Formulations ◽  
The Stability ◽  
Careful Distinction ◽  
Stable Vertex

This paper presents new insight into the robust stability analysis of families of matrices described by convex combinations of Hurwitz stable 'vertex' matrices. Significant new insight is provided that removes many misconceptions that currently prevail in this problem formulation. In this connection, careful distinction is made between 'Structured' and 'Unstructured' convex combinations of matrices. The convex combinations arising from an uncertain matrix with interval parameters is labeled as 'structured' convex combinations whereas the convex combinations of 'user specified' Hurwitz stable vertex matrices are labeled as 'unstructured' convex combinations. It is clearly shown that the convex combination property in matrix case is dictated more by the nature of the 'vertex' matrices rather than by simply assigning values to the coefficients of the combination. From this analysis, it is clearly established that 'structured' and 'unstructured' convex combinations are two entirely different problem formulations and one is not a special case of the other as it is currently believed. Thus even the solution algorithms for checking the stability of these matrix families are different. After establishing this distinction, this paper then concentrates on the 'unstructured' case and provides a 'vertex solution' to a specific three vertex convex combination problem. The algorithm is illustrated with several examples. This contribution suggests that there is still considerable research needed to appreciably enhance the knowledge base in the important area of robust stability analysis of matrix families which arise in various applications.

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