scholarly journals A new approach to the stability theory of functional differential systems

1983 ◽  
Vol 95 (2) ◽  
pp. 319-334 ◽  
Author(s):  
G.R. Shendge
Keyword(s):  
Stability Theory ◽  
Differential Systems ◽  
New Approach ◽  
Functional Differential Systems ◽  
Functional Differential ◽  
The Stability

scholarly journals Stability of functional differential systems applied to the model of testosterone regulation

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Alexander Domoshnitsky ◽  
Irina Volinsky ◽  
Olga Pinhasov ◽  
Marina Bershadsky
Keyword(s):  
Feedback Control ◽  
Differential System ◽  
Testosterone Level ◽  
Dimensional System ◽  
Cauchy Matrix ◽  
Differential Systems ◽  
Functional Differential Systems ◽  
Functional Differential ◽  
To Come ◽  
The Stability

AbstractIn this paper we propose a method for stability studies of functional differential systems. The idea of our method is to reduce the analysis of an n-dimensional system to one for an $(n+m)$(n+m)-dimensional system, where m is a natural number, to obtain stability and then to come back and make conclusions on the stability of the given n-dimensional system. As an example, a model describing testosterone by distributed inputs feedback control is considered. The aim of the regulation is to hold testosterone concentration above an appropriate level. The feedback control with integral term is proposed. We have to increase the testosterone level to the normal one. The control we proposed could destroy the stability of the model. That is why we have to choose the parameters of our distributed control, namely a dosage or intensity of assimilation of a medicine in a human body in such a form that the stability of our system is preserved. Thus the problem of regulation of testosterone level leads us to the stability analysis of the functional differential system describing a connection between the concentrations of hormones (GnRH), (LH), and testosterone (Te). Constructing the system, we discard the connections which seem nonessential. To estimate the effect of these connections is an important problem. We construct the Cauchy matrix of integro-differential system to estimate this influence.

scholarly journals Impulsive Stability of Stochastic Functional Differential Systems Driven by G-Brownian Motion

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 227
Author(s):  
Lijun Pan ◽  
Jinde Cao ◽  
Yong Ren
Keyword(s):  
Brownian Motion ◽  
Exponential Stability ◽  
Differential Systems ◽  
Stability Theorems ◽  
Functional Differential Systems ◽  
Functional Differential ◽  
The Stability ◽  
Delay Dependent ◽  
Moment Exponential Stability ◽  
Stochastic Functional

This paper is concerned with the p-th moment exponential stability and quasi sure exponential stability of impulsive stochastic functional differential systems driven by G-Brownian motion (IGSFDSs). By using G-Lyapunov method, several stability theorems of IGSFDSs are obtained. These new results are employed to impulsive stochastic delayed differential systems driven by G-motion (IGSDDEs). In addition, delay-dependent method is developed to investigate the stability of IGSDDSs by constructing the G-Lyapunov–Krasovkii functional. Finally, an example is given to demonstrate the effectiveness of the obtained results.

scholarly journals Exponential Stability of Impulsive Stochastic Functional Differential Systems with Delayed Impulses

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Fengqi Yao ◽  
Feiqi Deng ◽  
Pei Cheng
Keyword(s):  
Exponential Stability ◽  
Delay Systems ◽  
Differential Systems ◽  
Stochastic Delay ◽  
Functional Differential Systems ◽  
Two Measures ◽  
Functional Differential ◽  
The Stability ◽  
Delayed Impulses ◽  
Stochastic Functional

A class of generalized impulsive stochastic functional differential systems with delayed impulses is considered. By employing piecewise continuous Lyapunov functions and the Razumikhin techniques, several criteria on the exponential stability and uniform stability in terms of two measures for the mentioned systems are obtained, which show that unstable stochastic functional differential systems may be stabilized by appropriate delayed impulses. Based on the stability results, delayed impulsive controllers which mean square exponentially stabilize linear stochastic delay systems are proposed. Finally, numerical examples are given to verify the effectiveness and advantages of our results.

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