scholarly journals Sufficient Conditions for the Stability of Interval Systems with Multiple Time-Varying Delays

1997 ◽  
Vol 207 (1) ◽  
pp. 29-44 ◽  
Author(s):  
Yeong-Jeu Sun ◽  
Chien-Tien Lee ◽  
Jer-Guang Hsieh
Keyword(s):  
Sufficient Conditions ◽  
Multiple Time ◽  
Time Varying ◽  
The Stability ◽  
Interval Systems

scholarly journals Projective Synchronization Analysis of Drive-Response Coupled Dynamical Network with Multiple Time-Varying Delays via Impulsive Control

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Song Zheng
Keyword(s):  
Impulsive Control ◽  
Sufficient Conditions ◽  
Projective Synchronization ◽  
Multiple Time ◽  
Time Varying ◽  
Comparison Theory ◽  
Dynamical Network ◽  
Functional Differential ◽  
The Stability ◽  
System Nodes

The problem of projective synchronization of drive-response coupled dynamical network with delayed system nodes and multiple coupling time-varying delays is investigated. Some sufficient conditions are derived to ensure projective synchronization of drive-response coupled network under the impulsive controller by utilizing the stability analysis of the impulsive functional differential equation and comparison theory. Numerical simulations on coupled time delay Lorenz chaotic systems are exploited finally to illustrate the effectiveness of the obtained results.

Exponential stability and periodicity of memristor-based recurrent neural networks with time-varying delays

2017 ◽  
Vol 10 (02) ◽  
pp. 1750027 ◽  
Author(s):  
Wei Zhang ◽  
Chuandong Li ◽  
Tingwen Huang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Functional Approach ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Matrix Inequalities ◽  
Inclusion Theory ◽  
The Stability

In this paper, the stability and periodicity of memristor-based neural networks with time-varying delays are studied. Based on linear matrix inequalities, differential inclusion theory and by constructing proper Lyapunov functional approach and using linear matrix inequality, some sufficient conditions are obtained for the global exponential stability and periodic solutions of memristor-based neural networks. Finally, two illustrative examples are given to demonstrate the results.

scholarly journals Stability and stabilizability of dynamical systems with multiple time-varying delays: delay-dependent criteria

2003 ◽  
Vol 2003 (4) ◽  
pp. 137-152 ◽  
Author(s):  
D. Mehdi ◽  
E. K. Boukas
Keyword(s):  
Time Delays ◽  
Uncertain Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Multiple Time ◽  
Multiple Time Delays ◽  
The Stability ◽  
Delay Dependent ◽  
Bounded Uncertainties ◽  
Norm Bounded Uncertainties

This paper deals with the class of uncertain systems with multiple time delays. The stability and stabilizability of this class of systems are considered. Their robustness are also studied when the norm-bounded uncertainties are considered. Linear matrix inequality (LMIs) delay-dependent sufficient conditions for both stability and stabilizability and their robustness are established to check if a system of this class is stable and/or is stabilizable. Some numerical examples are provided to show the usefulness of the proposed results.

On Stability of a Nonlinear, Periodically Time Varying, Rotating Blade

2011 ◽  
Author(s):  
Fengxia Wang
Keyword(s):  
Steady State ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Multiple Time ◽  
Time Varying ◽  
Rotating Blade ◽  
Stability And Bifurcation ◽  
Geometric Stiffening ◽  
Rotational Motions ◽  
The Stability

This paper discusses the stability of a periodically time-varying, spinning blade with cubic geometric nonlinearity. The modal reduction method is adopted to simplify the nonlinear partial differential equations to the ordinary differential equations, and the geometric stiffening is approximated by the axial inertia membrane force. The method of multiple time scale is employed to study the steady state motions, the corresponding stability and bifurcation for such a periodically time-varying rotating blade. The backbone curves for steady-state motions are achieved, and the parameter map for stability and bifurcation is developed. Illustration of the steady-state motions is presented for an understanding of rotational motions of the rotating blade.

State feedback observer-based control design for linear descriptor systems with multiple time-varying delays

2020 ◽  
Vol 37 (4) ◽  
pp. 1218-1236
Author(s):  
V N Phat ◽  
P Niamsup ◽  
N H Muoi
Keyword(s):  
State Feedback ◽  
Design Method ◽  
Sufficient Conditions ◽  
Descriptor Systems ◽  
Linear Matrix ◽  
Multiple Time ◽  
Time Varying ◽  
Feedback Controllers ◽  
Delay Function ◽  
Delay Dependent

Abstract In this paper, we propose an linear matrix inequality (LMI)-based design method to observer-based control problem of linear descriptor systems with multiple time-varying delays. The delay function can be continuous and bounded but not necessarily differentiable. First, by introducing a new set of improved Lyapunov–Krasovskii functionals that avoid calculating the derivative of the delay function, we obtain new delay-dependent sufficient conditions for guaranteeing the system to be regular, impulse-free and asymptotically stable. Then, based on the derived stability conditions, we design state feedback controllers and observer gains via LMIs, which can be solved numerically in standard computational algorithms. A numerical example with simulation is given to demonstrate the efficiency and validity of the proposed deign.

Dynamic Stability of a Nonlinear Cylindrical Shell

1984 ◽  
Vol 51 (4) ◽  
pp. 852-856 ◽  
Author(s):  
A. Tylikowski
Keyword(s):  
Cylindrical Shell ◽  
Sufficient Conditions ◽  
Middle Surface ◽  
Elastic Cylindrical Shell ◽  
Time Varying ◽  
Liapunov Method ◽  
Linearized Problem ◽  
Nonlinear Shell ◽  
The Stability ◽  
Radial Loading

The stability of the undeflected middle surface of a uniform elastic cylindrical shell governed by Ka´rma´n’s equations is studied. The shell is being subjected to a time-varying axial compression as well as a uniformly distributed time-varying radial loading. Using the direct Liapunov method sufficient conditions for deterministic asymptotic as well as stochastic stability are obtained. A relation between stability conditions of a linearized problem and that of Ka´rma´n’s equations is found. Contrary to the stability theory of nonlinear plates it is established that the linearized problem should be modified to ensure the stability of the nonlinear shell. The case when the shell is governed by the Itoˆ stochastic nonlinear equations is also discussed.

Nonlinear Oscillation of a Rotor-AMB System With Time Varying Stiffness and Multi-External Excitations

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
M. Kamel ◽  
H. S. Bauomy
Keyword(s):  
Steady State ◽  
Order Approximation ◽  
Nonlinear Differential Equations ◽  
Steady State Solution ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Multiple Time ◽  
Time Varying ◽  
The Stability ◽  
Amb System

The rotor-active magnetic bearing system subjected to a periodically time-varying stiffness having quadratic and cubic nonlinearities is studied and solved. The multiple time scale technique is applied to solve the nonlinear differential equations governing the system up to the second order approximation. All possible resonance cases are deduced at this approximation and some of them are confirmed by applying the Rung–Kutta method. The main attention is focused on the stability of the steady-state solution near the simultaneous principal resonance and the effects of different parameters on the steady-state response. A comparison is made with the available published work.

scholarly journals Adaptive-Impulsive Control of the Projective Synchronization in Drive-Response Complex Dynamical Networks with Time-Varying Coupling

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Song Zheng
Keyword(s):  
Impulsive Control ◽  
Sufficient Conditions ◽  
Complex Dynamical Networks ◽  
Projective Synchronization ◽  
Time Varying ◽  
Dynamical Networks ◽  
Adaptive Feedback ◽  
Hybrid Controller ◽  
The Stability ◽  
Response Complex

This paper investigates the projective synchronization (PS) of drive-response time-varying coupling complex dynamical networks with time delay via an adaptive-impulsive controlling method, in which the weights of links are time varying. Based on the stability analysis of impulsive control system, sufficient conditions for the PS are derived, and a hybrid controller, that is, an adaptive feedback controller with impulsive control effects, is designed. Numerical simulations are performed to verify the correctness and effectiveness of theoretical result.

scholarly journals Stability of Stochastic Discrete-Time Neural Networks with Discrete Delays and the Leakage Delay

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Liyuan Hou ◽  
Hong Zhu
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Leakage Delay ◽  
Time Varying ◽  
Discrete Time System ◽  
Time System ◽  
Discrete Delays ◽  
The Stability

This paper investigates the stability of stochastic discrete-time neural networks (NNs) with discrete time-varying delays and leakage delay. As the partition of time-varying and leakage delay is brought in the discrete-time system, we construct a novel Lyapunov-Krasovskii function based on stability theory. Furthermore sufficient conditions are derived to guarantee the global asymptotic stability of the equilibrium point. Numerical example is given to demonstrate the effectiveness of the proposed method and the applicability of the proposed method.

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