Pulse-Width Relay Control in Sampling Systems

1961 ◽  
Vol 83 (1) ◽  
pp. 65-76 ◽  
Author(s):  
Winston L. Nelson
Keyword(s):  
Control Systems ◽  
Pulse Width ◽  
Sufficient Conditions ◽  
Sampling Period ◽  
Specific Design ◽  
Design Problems ◽  
Relay Control ◽  
Practical Design ◽  
Sampling Systems ◽  
Theoretical Results

The use of pulse-width control for the on-off regulation of systems subject to sampling is investigated in this paper. The inherent inability of simple on-off control to achieve accurate, or dead-beat control in sampling systems is demonstrated, and methods for predicting and minimizing the limit-cycle behavior of these systems are given. It is then shown that if the on-off control is modified by allowing control of the “on” time during each sampling period, it is possible to achieve asymptotically stable dead-beat control. Sufficient conditions for the asymptotic stability in the large of pulse-width control systems are developed, using the “second method” of Lyapunov. Practical design of pulse-width controllers is developed from the theoretical results and experimental evaluation is given for some specific design problems.

scholarly journals Stability Analysis of Impulsive Control Systems with Finite and Infinite Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Xuling Wang ◽  
Xiaodi Li ◽  
Gani Tr. Stamov
Keyword(s):  
Control Systems ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Stability Criteria ◽  
Numerical Examples ◽  
Infinite Delays ◽  
Impulsive Control Systems ◽  
Stable Matrix ◽  
Theoretical Results

This paper studies impulsive control systems with finite and infinite delays. Several stability criteria are established by employing the largest and smallest eigenvalue of matrix. Our sufficient conditions are less restrictive than the ones in the earlier literature. Moreover, it is shown that by using impulsive control, the delay systems can be stabilized even if it contains no stable matrix. Finally, some numerical examples are discussed to illustrate the theoretical results.

scholarly journals Stabilization for Networked Control Systems with Random Sampling Periods

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Yuan Li ◽  
Qingling Zhang ◽  
Shuanghong Zhang ◽  
Min Cai
Keyword(s):  
Markov Chains ◽  
Control Systems ◽  
Random Sampling ◽  
Networked Control Systems ◽  
Transition Probabilities ◽  
Sufficient Conditions ◽  
Sampling Period ◽  
Networked Control ◽  
Linear Matrix ◽  
Random Delays

This paper investigates the stabilization of networked control systems (NCSs) with random delays and random sampling periods. Sampling periods can randomly switch between three cases according to the high, low, and medium types of network load. The sensor-to-controller (S-C) random delays and random sampling periods are modeled as Markov chains. The transition probabilities of Markov chains do not need to be completely known. A state feedback controller is designed via the iterative linear matrix inequality (LMI) approach. It is shown that the designed controller is two-mode dependent and depends on not only the currentS-Cdelay but also the most recent available sampling period at the controller node. The resulting closed-loop systems are special discrete-time jump linear systems with two modes. The sufficient conditions for the stochastic stability are established. An example of the cart and inverted pendulum is given to illustrate the effectiveness of the theoretical result.

Conditions for the local and global asymptotic stability of the time–fractional Degn–Harrison system

2020 ◽  
Vol 21 (7-8) ◽  
pp. 749-759
Author(s):  
Rachida Mezhoud ◽  
Khaled Saoudi ◽  
Abderrahmane Zaraï ◽  
Salem Abdelmalek
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Linearization Method ◽  
Direct Lyapunov Method ◽  
Fractional Systems ◽  
Reaction Diffusion Model ◽  
Theoretical Results

AbstractFractional calculus has been shown to improve the dynamics of differential system models and provide a better understanding of their dynamics. This paper considers the time–fractional version of the Degn–Harrison reaction–diffusion model. Sufficient conditions are established for the local and global asymptotic stability of the model by means of invariant rectangles, the fundamental stability theory of fractional systems, the linearization method, and the direct Lyapunov method. Numerical simulation results are used to illustrate the theoretical results.

Relay Control Systems with Discrete Time Equalizer

2020 ◽  
Author(s):  
Oleksii Sheremet ◽  
Oleksandr Sadovoi ◽  
Kateryna Sheremet ◽  
Yuliia Sokhina
Keyword(s):  
Control Systems ◽  
Discrete Time ◽  
Relay Control

scholarly journals Results on the approximate controllability of fractional hemivariational inequalities of order $1< r<2$

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
M. Mohan Raja ◽  
V. Vijayakumar ◽  
Le Nhat Huynh ◽  
R. Udhayakumar ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Fixed Point ◽  
Control Systems ◽  
Approximate Controllability ◽  
Hemivariational Inequalities ◽  
Evolution Inclusions ◽  
Fractional Systems ◽  
Cosine Families ◽  
Fixed Point Approach ◽  
Semilinear Control Systems ◽  
Theoretical Results

AbstractIn this paper, we investigate the approximate controllability of fractional evolution inclusions with hemivariational inequalities of order $1< r<2$ 1 < r < 2 . The main results of this paper are verified by using the fractional theories, multivalued analysis, cosine families, and fixed-point approach. At first, we discuss the existence of the mild solution for the class of fractional systems. After that, we establish the approximate controllability of linear and semilinear control systems. Finally, an application is presented to illustrate our theoretical results.

Design Chaotic Neural Network from Discrete Time Feedback Function

2013 ◽  
Vol 339 ◽  
pp. 366-371
Author(s):  
Jin Sheng Ren ◽  
Guang Chun Luo ◽  
Ke Qin
Keyword(s):  
Discrete Time ◽  
Design Methodology ◽  
Universal Design ◽  
Jacobian Matrix ◽  
Sufficient Conditions ◽  
Neural Net ◽  
Chaotic Neural Network ◽  
Data Set ◽  
Dominant Matrix ◽  
Theoretical Results

The goal of this paper is to give a universal design methodology of a Chaotic Neural Net-work (CNN). By appropriately choosing self-feedback, coupling functions and external stimulus, we have succeeded in proving a dynamical system defined by discrete time feedback equations possess-ing interesting chaotic properties. The sufficient conditions of chaos are analyzed by using Jacobian matrix, diagonal dominant matrix and Lyapunov Exponent (LE). Experiments are also conducted un-der a simple data set. The results confirm the theorem's correctness. As far as we know, both the experimental and theoretical results presented here are novel.

scholarly journals Stability and Bogdanov-Takens Bifurcation of an SIS Epidemic Model with Saturated Treatment Function

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Yanju Xiao ◽  
Weipeng Zhang ◽  
Guifeng Deng ◽  
Zhehua Liu
Keyword(s):  
Sufficient Conditions ◽  
Global Dynamics ◽  
Sis Model ◽  
Delayed Treatment ◽  
Sis Epidemic Model ◽  
Treatment Function ◽  
Lyapunov Coefficient ◽  
Saturated Treatment ◽  
Theoretical Results ◽  
Disease Free

This paper introduces the global dynamics of an SIS model with bilinear incidence rate and saturated treatment function. The treatment function is a continuous and differential function which shows the effect of delayed treatment when the rate of treatment is lower and the number of infected individuals is getting larger. Sufficient conditions for the existence and global asymptotic stability of the disease-free and endemic equilibria are given in this paper. The first Lyapunov coefficient is computed to determine various types of Hopf bifurcation, such as subcritical or supercritical. By some complex algebra, the Bogdanov-Takens normal form and the three types of bifurcation curves are derived. Finally, mathematical analysis and numerical simulations are given to support our theoretical results.

scholarly journals Exponential Stability of Stochastic Differential Equation with Mixed Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Wenli Zhu ◽  
Jiexiang Huang ◽  
Xinfeng Ruan ◽  
Zhao Zhao
Keyword(s):  
Differential Equation ◽  
Time Delay ◽  
Stochastic Differential Equation ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Martingale Inequality ◽  
Mixed Delay ◽  
Exponentially Stable ◽  
Theoretical Results

This paper focuses on a class of stochastic differential equations with mixed delay based on Lyapunov stability theory, Itô formula, stochastic analysis, and inequality technique. A sufficient condition for existence and uniqueness of the adapted solution to such systems is established by employing fixed point theorem. Some sufficient conditions of exponential stability and corollaries for such systems are obtained by using Lyapunov function. By utilizing Doob’s martingale inequality and Borel-Cantelli lemma, it is shown that the exponentially stable in the mean square of such systems implies the almost surely exponentially stable. In particular, our theoretical results show that if stochastic differential equation is exponentially stable and the time delay is sufficiently small, then the corresponding stochastic differential equation with mixed delay will remain exponentially stable. Moreover, time delay upper limit is solved by using our theoretical results when the system is exponentially stable, and they are more easily verified and applied in practice.

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