On the stability theorem in failure-detection systems

1994 ◽  
Vol 82 (1) ◽  
pp. 189-190
Author(s):  
M. L. Ni ◽  
Y. Chen
Keyword(s):  
Failure Detection ◽  
Stability Theorem ◽  
Detection Systems ◽  
The Stability

Stability of elliptical horizontally inhomogeneous rodons

2000 ◽  
Vol 416 ◽  
pp. 29-43
Author(s):  
RENÉ PINET ◽  
E. G. PAVÍA
Keyword(s):  
Formal Analysis ◽  
Detailed Examination ◽  
Stability Theorem ◽  
Homogeneous Case ◽  
Density Distributions ◽  
Formal Stability ◽  
Inhomogeneous Density ◽  
Loss Of Mass ◽  
The Stability ◽  
Main Effects

The stability of one-layer vortices with inhomogeneous horizontal density distributions is examined both analytically and numerically. Attention is focused on elliptical vortices for which the formal stability theorem proved by Ochoa, Sheinbaum & Pavía (1988) does not apply. Our method closely follows that of Ripa (1987) developed for the homogeneous case; and indeed they yield the same results when inhomogenities vanish. It is shown that a criterion from the formal analysis – the necessity of a radial increase in density for instability – does not extend to elliptical vortices. In addition, a detailed examination of the evolution of the inhomogeneous density fields, provided by numerical simulations, shows that homogenization, axisymmetrization and loss of mass to the surroundings are the main effects of instability.

scholarly journals HUR-approximation of an ELTA functional equation

Filomat ◽  
2020 ◽  
Vol 34 (13) ◽  
pp. 4311-4328
Author(s):  
A.R. Sharifi ◽  
Azadi Kenary ◽  
B. Yousefi ◽  
R. Soltani
Keyword(s):  
Functional Equation ◽  
Banach Spaces ◽  
Linear Mapping ◽  
Stability Theorem ◽  
Normed Spaces ◽  
The Stability ◽  
Rassias Stability

The main goal of this paper is study of the Hyers-Ulam-Rassias stability (briefly HUR-approximation) of the following Euler-Lagrange type additive(briefly ELTA) functional equation ?nj=1f (1/2 ?1?i?n,i?j rixi- 1/2 rjxj) + ?ni=1 rif(xi)=nf (1/2 ?ni=1 rixi) where r1,..., rn ? R, ?ni=k rk?0, and ri,rj?0 for some 1? i < j ? n, in fuzzy normed spaces. The concept of HUR-approximation originated from Th. M. Rassias stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.

The ?-stability theorem for flows

1970 ◽  
Vol 11 (2) ◽  
pp. 150-158 ◽  
Author(s):  
Charles Pugh ◽  
Michael Shub
Keyword(s):  
Stability Theorem ◽  
The Stability

scholarly journals Generalized Hyers–Ulam Stability of the Additive Functional Equation

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 76 ◽  
Author(s):  
Yang-Hi Lee ◽  
Gwang Kim
Keyword(s):  
Functional Equation ◽  
Additive Function ◽  
Additive Functional ◽  
Stability Theorem ◽  
Ulam Stability ◽  
Additive Functional Equation ◽  
Stability Theorems ◽  
The Stability

We will prove the generalized Hyers–Ulam stability and the hyperstability of the additive functional equation f(x1 + y1, x2 + y2, …, xn + yn) = f(x1, x2, … xn) + f(y1, y2, …, yn). By restricting the domain of a mapping f that satisfies the inequality condition used in the assumption part of the stability theorem, we partially generalize the results of the stability theorems of the additive function equations.

Stability theorems

1977 ◽  
Vol 9 (02) ◽  
pp. 336-361 ◽  
Author(s):  
Eugene Lukacs
Keyword(s):  
Stability Theorem ◽  
Stability Theorems ◽  
Primary Object ◽  
The Stability ◽  
Decomposition Theorems

A stability theorem determines the extent to which the conclusions of a given theorem are affected if the assumptions of the theorem are not exactly but only approximately satisfied. The meaning of the word ‘approximately’ has to be defined exactly. The stability of decomposition theorems, of characterizations by independence and by regression properties are the primary object of the paper.

Estimates of the Distance to the Set of Solenoidal Vector Fields and Applications to A Posteriori Error Control

2015 ◽  
Vol 15 (4) ◽  
pp. 515-530 ◽  
Author(s):  
Sergey Repin
Keyword(s):  
Error Control ◽  
Vector Fields ◽  
Bounded Operator ◽  
Posteriori Error ◽  
Stability Theorem ◽  
A Posteriori ◽  
Solenoidal Vector ◽  
Bounded Lipschitz Domain ◽  
Incompressible Viscous Fluids ◽  
The Stability

AbstractThe paper is concerned with computable estimates of the distance between a vector-valued function in the Sobolev space$W^{1,\gamma }(\Omega ,\mathbb {R}^d)$(where${\gamma \in (1,+\infty )}$and Ω is a bounded Lipschitz domain in ℝd) and the subspace${S^{1,\gamma }(\Omega ,\mathbb {R}^d)}$containing all divergence-free (solenoidal) vector functions. Derivation of these estimates is closely related to the stability theorem that establishes existence of a bounded operator inverse to the operator${\operatorname{div}}$. The constant in the respective stability inequality arises in the estimates of the distance to the set${S^{1,\gamma }(\Omega ,\mathbb {R}^d)}$. In general, it is difficult to find a guaranteed and realistic upper bound of this global constant. We suggest a way to circumvent this difficulty by using weak (integral mean) solenoidality conditions and localized versions of the stability theorem. They are derived for the case where Ω is represented as a union of simple subdomains (overlapping or non-overlapping), for which estimates of the corresponding stability constants are known. These new versions of the stability theorem imply estimates of the distance to${S^{1,\gamma }(\Omega ,\mathbb {R}^d)}$that involve only local constants associated with subdomains. Finally, the estimates are used for deriving fully computable a posteriori estimates for problems in the theory of incompressible viscous fluids.

Anti-Synchronization Control of the Complex Lu System

2014 ◽  
Vol 721 ◽  
pp. 269-272
Author(s):  
Fan Di Zhang
Keyword(s):  
Complex System ◽  
Fractional Order ◽  
Control Strategy ◽  
Stability Theorem ◽  
Projective Synchronization ◽  
Synchronization Control ◽  
Fractional Order Systems ◽  
Lü System ◽  
The Stability ◽  
Lu System

This paper propose fractional-order Lu complex system. Moreover, projective synchronization control of the fractional-order hyper-chaotic complex Lu system is studied based on feedback technique and the stability theorem of fractional-order systems, the scheme of anti-synchronization for the fractional-order hyper-chaotic complex Lu system is presented. Numerical simulations on examples are presented to show the effectiveness of the proposed control strategy.

Identification and Adaptive Control of the Uncertain Lorenz System

2005 ◽  
Author(s):  
Hossein Nejat Pishkenari ◽  
Mohammad Shahrokhi
Keyword(s):  
Lorenz System ◽  
Rapid Identification ◽  
Open Loop ◽  
Stability Theorem ◽  
Lyapunov Stability Theorem ◽  
Unknown Parameters ◽  
Identification Method ◽  
System A ◽  
Identification Technique ◽  
The Stability

In this paper an identification method which can estimate the unknown parameters of a general nonlinear system based on three techniques (gradient, least-squares and rapid identification) has been developed. The stability of the proposed schemes has been shown using the Lyapunov stability theorem. The properties of each identification technique have been discussed briefly. Open loop identification of the Lorenz chaotic system is presented to show the effectiveness of the proposed approach. To illustrate the efficiency of the identification method for control purposes, it has been applied for controlling the well-known Lorenz system. By exploiting the property of the system a novel singularity-free controller is proposed. The stability of controller has been shown by a Lyapunov function. The designed controller coupled with the proposed identification technique can stabilize the uncertain Lorenz system. The effectiveness of the approach has been shown through simulation.

LAG SYNCHRONIZATION OF THE FRACTIONAL-ORDER SYSTEM VIA NONLINEAR OBSERVER

2011 ◽  
Vol 25 (29) ◽  
pp. 3951-3964 ◽  
Author(s):  
HAO ZHU ◽  
ZHONGSHI HE ◽  
SHANGBO ZHOU
Keyword(s):  
Numerical Simulation ◽  
Fractional Order ◽  
Stability Theorem ◽  
Nonlinear Observer ◽  
Order System ◽  
Fractional Order Systems ◽  
Lag Synchronization ◽  
Systematic Method ◽  
Fractional System ◽  
The Stability

In this paper, based on the idea of nonlinear observer, lag synchronization of chaotic fractional system with commensurate and incommensurate order is studied by the stability theorem of linear fractional-order systems. The theoretical analysis of fractional-order systems in this paper is a systematic method. This technique is applied to achieve the lag synchronization of fractional-order Rössler's system, verified by numerical simulation.

Stability theorems

1977 ◽  
Vol 9 (2) ◽  
pp. 336-361 ◽  
Author(s):  
Eugene Lukacs
Keyword(s):  
Stability Theorem ◽  
Stability Theorems ◽  
Primary Object ◽  
The Stability ◽  
Decomposition Theorems

A stability theorem determines the extent to which the conclusions of a given theorem are affected if the assumptions of the theorem are not exactly but only approximately satisfied. The meaning of the word ‘approximately’ has to be defined exactly. The stability of decomposition theorems, of characterizations by independence and by regression properties are the primary object of the paper.

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