Representation of Solutions and Finite Time Stability for Delay Differential Systems with Impulsive Effects

2019 ◽  
Vol 20 (2) ◽  
pp. 205-221 ◽  
Author(s):  
Zhongli You ◽  
JinRong Wang ◽  
Yong Zhou ◽  
Michal Fečkan
Keyword(s):  
Finite Time ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Time Stability ◽  
Finite Time Stability ◽  
Representation Of Solutions ◽  
Variation Of Constants ◽  
Impulsive Delay ◽  
Delay Differential Systems ◽  
Delay Differential

AbstractIn this paper, we study finite time stability for linear and nonlinear delay systems with linear impulsive conditions and linear parts defined by permutable matrices. We introduce a new concept of impulsive delayed matrix function and apply the variation of constants method to seek a representation of solution of linear impulsive delay systems, which can be well used to deal with finite time stability. We establish sufficient conditions for the finite time stability results by using the properties of impulsive delayed matrix exponential and Gronwall’s integral inequalities. Finally, we give numerical examples to demonstrate the validity of theoretical results and present some possible advantage by comparing the current work with the previous literature.

Finite time stability of semilinear multi-delay differential systems

2017 ◽  
Vol 40 (9) ◽  
pp. 2948-2959
Author(s):  
JinRong Wang ◽  
Zijian Luo
Keyword(s):  
Finite Time ◽  
Sufficient Conditions ◽  
Time Stability ◽  
Differential Systems ◽  
Finite Time Stability ◽  
Alternative Approach ◽  
Representation Of Solutions ◽  
Delay Differential Systems ◽  
Delay Differential ◽  
Exponential Matrix

In this paper, we provide an alternative approach to study finite time stability for semilinear multi-delay differential systems with pairwise permutable matrices associated with the stand and generalized Landau symbol conditions for nonlinear terms. The explicit representation of solutions involving a special multi-delayed exponential matrix function is developed to establish sufficient conditions to guarantee the systems are finite time stable by virtue of Gronwall integral inequalities with delay. Finally, we demonstrate the validity of the designed method and discuss it using numerical examples.

scholarly journals Stability of singular time-delay systems in the sense of non-Lyapunov: Classical and modern approach

2013 ◽  
Vol 67 (2) ◽  
pp. 193-202 ◽  
Author(s):  
Dragutin Debeljkovic ◽  
Sreten Stojanovic ◽  
Marko Aleksendric
Keyword(s):  
Time Delay ◽  
Finite Time ◽  
Initial Conditions ◽  
Sufficient Conditions ◽  
Practical Stability ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Time Stability ◽  
Modern Approach ◽  
Finite Time Stability

This paper provides sufficient conditions for both practical stability and finite-time stability of linear singular continuous time-delay systems which can be mathematically described as Ex(t)=Aox(t)+A1x(t-t). Considering a finite-time stability concept, new delay independent and delay dependent conditions have been derived using the approach based on the Lyapunov-like functions and their properties on the subspace of consistent initial conditions. These functions do not need to have the properties of positivity in the whole state space and negative derivatives along the system trajectories. When the practical stability has been analyzed the above mentioned approach was combined and supported by the classical Lyapunov technique to guarantee the attractivity property of the system behavior. Moreover an linear matrix inequality (LMI) approach has been applied in order to get less conservative conditions.

scholarly journals Finite-Time Stability of Neutral Fractional Time-Delay Systems via Generalized Gronwalls Inequality

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Pang Denghao ◽  
Jiang Wei
Keyword(s):  
Time Delay ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Gronwall Inequality ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Time Stability ◽  
Finite Time Stability ◽  
Generalized Gronwall Inequality ◽  
Grönwall Inequality

This paper studies the finite-time stability of neutral fractional time-delay systems. With the generalized Gronwall inequality, sufficient conditions of the finite-time stability are obtained for the particular class of neutral fractional time-delay systems.

scholarly journals On necessary and sufficient conditions for output finite-time stability

Automatica ◽  
2021 ◽  
Vol 125 ◽  
pp. 109427
Author(s):  
Konstantin Zimenko ◽  
Denis Efimov ◽  
Andrey Polyakov ◽  
Artem Kremlev
Keyword(s):  
Finite Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Time Stability ◽  
Finite Time Stability ◽  
Necessary And Sufficient

scholarly journals Finite-TimeH∞Control for Time-Delayed Stochastic Systems with Markovian Switching

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Wenhua Gao ◽  
Feiqi Deng ◽  
Ruiqiu Zhang ◽  
Wenhui Liu
Keyword(s):  
Finite Time ◽  
State Feedback ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Markovian Switching ◽  
Time Stability ◽  
Finite Time Stability ◽  
Weighting Matrix ◽  
Simulation Results ◽  
Dependent State

This paper studies the problem of finite-timeH∞control for time-delayed Itô stochastic systems with Markovian switching. By using the appropriate Lyapunov-Krasovskii functional and free-weighting matrix techniques, some sufficient conditions of finite-time stability for time-delayed stochastic systems with Markovian switching are proposed. Based on constructing new Lyapunov-Krasovskii functional, the mode-dependent state feedback controller for the finite-timeH∞control is obtained. Simulation results illustrate the effectiveness of the proposed method.

scholarly journals Finite-Time Synchronization of Complex Dynamical Networks with Time-Varying Delays and Nonidentical Nodes

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Ahmadjan Muhammadhaji ◽  
Abdujelil Abdurahman ◽  
Haijun Jiang
Keyword(s):  
Complex Networks ◽  
Finite Time ◽  
Time Synchronization ◽  
Sufficient Conditions ◽  
Time Stability ◽  
Finite Time Stability ◽  
Uniformly Smooth ◽  
Nonidentical Nodes ◽  
Smooth State ◽  
Synchronization Performance

In this paper, we investigated the finite-time synchronization (FTS) problem for a class of time-delayed complex networks with nonidentical nodes onto any uniformly smooth state. By employing the finite-time stability theorem and designing two types of novel controllers, we obtained some simple sufficient conditions for the FTS of addressed complex networks. Furthermore, we also analyzed the effects of control variables on synchronization performance. Finally, we showed the effectiveness and feasibility of our methods by giving two numerical examples.

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