Computers and Mathematics with Applications, ISSN 0898-1221, 09/2012, Volume 64, Issue 6, pp. 1875 - 1881

An impulsive delay differential inequality is formulated in this paper. An estimate of the rate of decay of solutions to this inequality is obtained. It can be...

Global exponential stability | Impulsive control law (ICL) | Impulsive differential inequality | Linear matrix inequality (LMI) | Time-varying delay | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | DISTRIBUTED DELAYS | CONTROL-SYSTEMS | EQUATIONS | TIME-VARYING DELAYS | BAM NEURAL-NETWORKS | Control systems | Equality

Global exponential stability | Impulsive control law (ICL) | Impulsive differential inequality | Linear matrix inequality (LMI) | Time-varying delay | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | DISTRIBUTED DELAYS | CONTROL-SYSTEMS | EQUATIONS | TIME-VARYING DELAYS | BAM NEURAL-NETWORKS | Control systems | Equality

Journal Article

Neurocomputing, ISSN 0925-2312, 05/2019, Volume 341, pp. 99 - 106

Impulsive differential inequality is crucial for nonlinear impulsive differential system. In this paper, an impulsive delayed integro-differential inequality...

Memristive neural networks | Discrete-distributed delays | Exponential stability | Impulsive integro-differential inequality | MEMRISTIVE NEURAL-NETWORKS | EXISTENCE | SYNCHRONIZATION | DESIGN | SYSTEMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Neural networks | Equality

Memristive neural networks | Discrete-distributed delays | Exponential stability | Impulsive integro-differential inequality | MEMRISTIVE NEURAL-NETWORKS | EXISTENCE | SYNCHRONIZATION | DESIGN | SYSTEMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Neural networks | Equality

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2011, Volume 2011, Issue 1, pp. 1 - 8

In this article, a new nonlinear impulsive delay differential inequality is established, which can be applied in the dynamical analysis of nonlinear systems to...

nonlinear functional differential systems | Analysis | Impulsive delay differential inequality | Mathematics, general | Mathematics | Applications of Mathematics | exponential stability | Exponential stability | Nonlinear functional differential systems | GLOBAL EXPONENTIAL STABILITY | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | LYAPUNOV-RAZUMIKHIN METHOD | NEURAL-NETWORKS | EQUATIONS | SYSTEMS | ASYMPTOTIC STABILITY | Nonlinear dynamics | Stability | Inequalities | Differential equations | Nonlinearity | Dynamical systems | Delay

nonlinear functional differential systems | Analysis | Impulsive delay differential inequality | Mathematics, general | Mathematics | Applications of Mathematics | exponential stability | Exponential stability | Nonlinear functional differential systems | GLOBAL EXPONENTIAL STABILITY | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | LYAPUNOV-RAZUMIKHIN METHOD | NEURAL-NETWORKS | EQUATIONS | SYSTEMS | ASYMPTOTIC STABILITY | Nonlinear dynamics | Stability | Inequalities | Differential equations | Nonlinearity | Dynamical systems | Delay

Journal Article

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Nonlinear impulsive differential and integral inequalities with nonlocal jump conditions

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2018, Volume 2018, Issue 1, pp. 1 - 22

Some new nonlinear impulsive differential and integral inequalities with nonlocal integral jump conditions are presented in this paper. Using the method of...

Nonlocal intergal jump conditions | Nonlinear impulsive | Riemann–Liouville fractional derivative | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | Differential and integral inequalities | MATHEMATICS | MATHEMATICS, APPLIED | Riemann-Liouville fractional derivative | DELAY | Upper bounds | Integrals | Inequalities | Research

Nonlocal intergal jump conditions | Nonlinear impulsive | Riemann–Liouville fractional derivative | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | Differential and integral inequalities | MATHEMATICS | MATHEMATICS, APPLIED | Riemann-Liouville fractional derivative | DELAY | Upper bounds | Integrals | Inequalities | Research

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Nonlinear impulsive differential and integral inequalities with integral jump conditions

Advances in Difference Equations, ISSN 1687-1839, 12/2016, Volume 2016, Issue 1, pp. 1 - 13

Some new nonlinear impulsive differential inequalities and integral inequalities with integral jump conditions for discontinuous functions are established...

34A37 | discontinuous function | Mathematics | integral jump condition | Ordinary Differential Equations | impulsive differential system | Functional Analysis | Analysis | Difference and Functional Equations | Mathematics, general | integral inequalities | 34A40 | Partial Differential Equations | MATHEMATICS | MATHEMATICS, APPLIED | DELAY | Nonlinearity | Qualitative analysis | Difference equations | Integrals | Inequalities

34A37 | discontinuous function | Mathematics | integral jump condition | Ordinary Differential Equations | impulsive differential system | Functional Analysis | Analysis | Difference and Functional Equations | Mathematics, general | integral inequalities | 34A40 | Partial Differential Equations | MATHEMATICS | MATHEMATICS, APPLIED | DELAY | Nonlinearity | Qualitative analysis | Difference equations | Integrals | Inequalities

Journal Article

Advances in Difference Equations, ISSN 1687-1839, 12/2018, Volume 2018, Issue 1, pp. 1 - 16

In this paper, we establish some new integral inequalities with mixed nonlinearities for discontinuous functions, which provide a handy tool in deriving the...

Ordinary Differential Equations | Functional Analysis | Analysis | Difference and Functional Equations | discontinuous functions | Mathematics, general | mixed nonlinearities | Mathematics | integral inequalities | Partial Differential Equations | impulsive differential equations | MATHEMATICS | MATHEMATICS, APPLIED | BELLMAN-BIHARI TYPE | VARIABLES

Ordinary Differential Equations | Functional Analysis | Analysis | Difference and Functional Equations | discontinuous functions | Mathematics, general | mixed nonlinearities | Mathematics | integral inequalities | Partial Differential Equations | impulsive differential equations | MATHEMATICS | MATHEMATICS, APPLIED | BELLMAN-BIHARI TYPE | VARIABLES

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2018, Volume 2018, Issue 1, pp. 1 - 14

We establish some new noninstantaneous impulsive inequalities using the conformable fractional calculus.

34A37 | Conformable fractional integral | Impulsive inequalities | 26D10 | Analysis | Conformable fractional derivative | 26A33 | Mathematics, general | Mathematics | Applications of Mathematics | MATHEMATICS | MATHEMATICS, APPLIED | DIFFERENTIAL-EQUATIONS | Fractional calculus | Inequalities | Research

34A37 | Conformable fractional integral | Impulsive inequalities | 26D10 | Analysis | Conformable fractional derivative | 26A33 | Mathematics, general | Mathematics | Applications of Mathematics | MATHEMATICS | MATHEMATICS, APPLIED | DIFFERENTIAL-EQUATIONS | Fractional calculus | Inequalities | Research

Journal Article

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Impulsive differential and impulsive integral inequalities with integral jump conditions

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2012, Volume 2012, Issue 1, pp. 1 - 11

In this article, we establish some impulsive differential and impulsive integral inequalities for integral jump conditions. The new jump conditions for impulse...

integral condition | impulsive differential inequality | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | impulsive integral inequality | Integral condition | Impulsive integral inequality | Impulsive differential inequality | MATHEMATICS | FORCED OSCILLATION | MATHEMATICS, APPLIED | QUASI-LINEARIZATION | BOUNDARY-VALUE-PROBLEMS | SYSTEMS | INTEGRODIFFERENTIAL EQUATIONS | MAXIMUM-PRINCIPLES

integral condition | impulsive differential inequality | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | impulsive integral inequality | Integral condition | Impulsive integral inequality | Impulsive differential inequality | MATHEMATICS | FORCED OSCILLATION | MATHEMATICS, APPLIED | QUASI-LINEARIZATION | BOUNDARY-VALUE-PROBLEMS | SYSTEMS | INTEGRODIFFERENTIAL EQUATIONS | MAXIMUM-PRINCIPLES

Journal Article

International Journal of Adaptive Control and Signal Processing, ISSN 0890-6327, 09/2018, Volume 32, Issue 9, pp. 1294 - 1312

Summary This paper investigates the global asymptotic stability analysis for a class of complex‐valued neural networks with leakage delay and interval...

leakage delay | interval time‐varying delays | complex‐valued neural networks | global asymptotic stability | complex-valued neural networks | interval time-varying delays | TO-STATE STABILITY | EXPONENTIAL STABILITY | IMPULSIVE CONTROL | PASSIVITY ANALYSIS | ROBUST STABILITY | DISSIPATIVITY ANALYSIS | NONLINEAR DIFFERENTIAL-SYSTEMS | MULTISTABILITY | ENGINEERING, ELECTRICAL & ELECTRONIC | LAG SYNCHRONIZATION | CRITERION | AUTOMATION & CONTROL SYSTEMS | Neural networks | Analysis | Equality | Leakage | Computer simulation | Stabilization | Asymptotic properties | Mathematical analysis | Control systems | Stability analysis | Mathematical models | Linear matrix inequalities | Matrix methods | Delay

leakage delay | interval time‐varying delays | complex‐valued neural networks | global asymptotic stability | complex-valued neural networks | interval time-varying delays | TO-STATE STABILITY | EXPONENTIAL STABILITY | IMPULSIVE CONTROL | PASSIVITY ANALYSIS | ROBUST STABILITY | DISSIPATIVITY ANALYSIS | NONLINEAR DIFFERENTIAL-SYSTEMS | MULTISTABILITY | ENGINEERING, ELECTRICAL & ELECTRONIC | LAG SYNCHRONIZATION | CRITERION | AUTOMATION & CONTROL SYSTEMS | Neural networks | Analysis | Equality | Leakage | Computer simulation | Stabilization | Asymptotic properties | Mathematical analysis | Control systems | Stability analysis | Mathematical models | Linear matrix inequalities | Matrix methods | Delay

Journal Article

International Journal of Applied Mathematics and Computer Science, ISSN 1641-876X, 03/2013, Volume 23, Issue 1, pp. 201 - 211

This paper is devoted to studying the globally exponential stability of impulsive high-order Hopfield-type neural networks with time-varying delays. In the...

impulsive differential inequality | globally exponential stability | high-order Hopfield-type neural network | High-order Hopfield-type neural network | Impulsive differential inequality | Globally exponential stability | GLOBAL EXPONENTIAL STABILITY | CRITERIA | MATHEMATICS, APPLIED | STABILIZATION | TIME-VARYING DELAYS | HYBRID SYSTEMS | AUTOMATION & CONTROL SYSTEMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

impulsive differential inequality | globally exponential stability | high-order Hopfield-type neural network | High-order Hopfield-type neural network | Impulsive differential inequality | Globally exponential stability | GLOBAL EXPONENTIAL STABILITY | CRITERIA | MATHEMATICS, APPLIED | STABILIZATION | TIME-VARYING DELAYS | HYBRID SYSTEMS | AUTOMATION & CONTROL SYSTEMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Journal Article

Physics Letters A, ISSN 0375-9601, 2006, Volume 359, Issue 2, pp. 129 - 137

In this Letter, we establish a method to study the exponential p-stability of the zero solution of impulsive stochastic differential equations with delays. By...

Exponential p-stability | L-operator inequality | Stochastic | Impulsive | Delay | impulsive | delay | NEURAL-NETWORKS | PHYSICS, MULTIDISCIPLINARY | exponential p-stability | RAZUMIKHIN-TYPE THEOREMS | MEAN-SQUARE

Exponential p-stability | L-operator inequality | Stochastic | Impulsive | Delay | impulsive | delay | NEURAL-NETWORKS | PHYSICS, MULTIDISCIPLINARY | exponential p-stability | RAZUMIKHIN-TYPE THEOREMS | MEAN-SQUARE

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2016, Volume 2016, Issue 1, pp. 1 - 14

In this paper, some new generalized retarded inequalities for discontinuous functions are discussed, which are effective in dealing with the qualitative theory...

estimation | global existence | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | retarded differential-integral equation | impulsive equation | MATHEMATICS | MATHEMATICS, APPLIED | GRONWALL-LIKE INEQUALITY | Dealing | Integrals | Integral equations | Inequalities | Differential equations

estimation | global existence | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | retarded differential-integral equation | impulsive equation | MATHEMATICS | MATHEMATICS, APPLIED | GRONWALL-LIKE INEQUALITY | Dealing | Integrals | Integral equations | Inequalities | Differential equations

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 03/2018, Volume 64, Issue 3, pp. 1825 - 1844

Recent studies found that many channels are affected by additive noise that is impulsive in nature and is best explained by heavy-tailed symmetric alpha-stable...

Parameter estimation | Interference | Tools | Cramer-Rao bound | upper bounds | Impulsive noise | Fisher information inequality | Entropy | Noise measurement | Fisher information | estimation | de Bruijn identity | Power measurement | Cramer-Rao bounds | differential entropy of sums | isoperimetric inequality | alpha-stable | power | SUMSET | COMPUTER SCIENCE, INFORMATION SYSTEMS | POWER INEQUALITY | MATHEMATICAL-THEORY | RANDOM-VARIABLES | ENGINEERING, ELECTRICAL & ELECTRONIC | ENTROPY INEQUALITIES | POISSON FIELD | INTERFERENCE | RENYI ENTROPY | STABLE-DISTRIBUTIONS | Random noise | Channel capacity | Noise | Upper bounds | Inequalities | Gaussian distribution | Hilbert space | Random variables | Probability density functions

Parameter estimation | Interference | Tools | Cramer-Rao bound | upper bounds | Impulsive noise | Fisher information inequality | Entropy | Noise measurement | Fisher information | estimation | de Bruijn identity | Power measurement | Cramer-Rao bounds | differential entropy of sums | isoperimetric inequality | alpha-stable | power | SUMSET | COMPUTER SCIENCE, INFORMATION SYSTEMS | POWER INEQUALITY | MATHEMATICAL-THEORY | RANDOM-VARIABLES | ENGINEERING, ELECTRICAL & ELECTRONIC | ENTROPY INEQUALITIES | POISSON FIELD | INTERFERENCE | RENYI ENTROPY | STABLE-DISTRIBUTIONS | Random noise | Channel capacity | Noise | Upper bounds | Inequalities | Gaussian distribution | Hilbert space | Random variables | Probability density functions

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 2009, Volume 71, Issue 12, pp. e2276 - e2287

In this article we present some new nonlinear Bellman–Bihari type integral inequalities with delay for discontinuous functions (integro-sum inequalities;...

Discontinuous functions | Impulsive differential systems | Integral inequalities | Estimates | MATHEMATICS | MATHEMATICS, APPLIED | MOTION | STABILITY | SEVERAL-VARIABLES | IMPULSIVE DIFFERENTIAL-SYSTEMS | Impulses | Stability | Integrals | Differential equations | Inequalities | Nonlinearity | Delay

Discontinuous functions | Impulsive differential systems | Integral inequalities | Estimates | MATHEMATICS | MATHEMATICS, APPLIED | MOTION | STABILITY | SEVERAL-VARIABLES | IMPULSIVE DIFFERENTIAL-SYSTEMS | Impulses | Stability | Integrals | Differential equations | Inequalities | Nonlinearity | Delay

Journal Article

Nonlinear Analysis: Real World Applications, ISSN 1468-1218, 2010, Volume 11, Issue 5, pp. 4431 - 4441

In this paper, we investigate the existence of solutions to the boundary-value problem for impulsive differential equations. The ideas include variational...

Critical point | Mountain pass theorem | Iterative methods | Impulsive differential equations | Poincaré inequality | Poincar inequality | MATHEMATICS, APPLIED | Poincare inequality | GLOBAL ATTRACTIVITY | PULSE VACCINATION | MULTIPLE POSITIVE SOLUTIONS | DELAYED EPIDEMIC MODEL

Critical point | Mountain pass theorem | Iterative methods | Impulsive differential equations | Poincaré inequality | Poincar inequality | MATHEMATICS, APPLIED | Poincare inequality | GLOBAL ATTRACTIVITY | PULSE VACCINATION | MULTIPLE POSITIVE SOLUTIONS | DELAYED EPIDEMIC MODEL

Journal Article

Indagationes Mathematicae, ISSN 0019-3577, 01/2016, Volume 27, Issue 1, pp. 1 - 10

In this article, some new explicit bounds on solutions to a class of new nonlinear integral inequalities of Gronwall–Bellman–Bihari type with delay for...

Discontinuous functions | Impulsive differential systems | Integral inequalities | Gronwall–Bellman–Bihari type inequalities | Gronwall-Bellman-Bihari type inequalities | MATHEMATICS | TIME SCALES | EQUATIONS | EXPLICIT BOUNDS

Discontinuous functions | Impulsive differential systems | Integral inequalities | Gronwall–Bellman–Bihari type inequalities | Gronwall-Bellman-Bihari type inequalities | MATHEMATICS | TIME SCALES | EQUATIONS | EXPLICIT BOUNDS

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 2007, Volume 67, Issue 5, pp. 1550 - 1559

In this article we present new integral Gronwall–Bellman–Bihari type inequalities for discontinuous functions (integro-sum inequalities). As applications, we...

Discontinuous functions | Impulsive differential systems | Integral inequalities | Estimates | impulsive differential systems | MATHEMATICS | MATHEMATICS, APPLIED | MOTION | STABILITY | discontinuous functions | EQUATIONS | integral inequalities | estimates | INTEGRAL-INEQUALITIES

Discontinuous functions | Impulsive differential systems | Integral inequalities | Estimates | impulsive differential systems | MATHEMATICS | MATHEMATICS, APPLIED | MOTION | STABILITY | discontinuous functions | EQUATIONS | integral inequalities | estimates | INTEGRAL-INEQUALITIES

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 2009, Volume 57, Issue 1, pp. 54 - 61

In this paper, a nonlinear and nonautonomous impulsive stochastic functional differential equation is considered. By establishing an L -operator differential...

[formula omitted]-invariant set | Stochastic | [formula omitted]-operator inequality | Impulsive | [formula omitted]-attracting set | P-attracting set | L-operator inequality | P-invariant set | MATHEMATICS, APPLIED | STABILITY | DELAYS | SYSTEMS | MANIFOLDS | ASYMPTOTIC-BEHAVIOR | Nonlinearity | Mathematical models | Stochasticity | Differential equations | Inequalities

[formula omitted]-invariant set | Stochastic | [formula omitted]-operator inequality | Impulsive | [formula omitted]-attracting set | P-attracting set | L-operator inequality | P-invariant set | MATHEMATICS, APPLIED | STABILITY | DELAYS | SYSTEMS | MANIFOLDS | ASYMPTOTIC-BEHAVIOR | Nonlinearity | Mathematical models | Stochasticity | Differential equations | Inequalities

Journal Article

Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 10/2019, Volume 77, pp. 312 - 323

•We formulate the state-dependent impulsive differential equations (SDIDE) with saturation.•The existence of solution for the system and some sufficient...

Quasi-exponential stability | Collision surface | Impulsive differential equations (IDE) | Saturation | State-dependent impulses | Differential equations

Quasi-exponential stability | Collision surface | Impulsive differential equations (IDE) | Saturation | State-dependent impulses | Differential equations

Journal Article

Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 01/2013, Volume 18, Issue 1, pp. 28 - 41

► A generalized anti-periodic boundary value problem for an impulsive fractional differential equation is studied. ► A natural formula of solutions is derived...

Impulsive fractional differential equations | Anti-periodic | Boundary value problems | Hybrid singular type Gronwall inequality | Solutions | EXISTENCE | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | PHYSICS, FLUIDS & PLASMAS | PHYSICS, MATHEMATICAL | Differential equations | Computer simulation | Existence theorems | Mathematical analysis | Inequalities | Nonlinearity | Mathematical models

Impulsive fractional differential equations | Anti-periodic | Boundary value problems | Hybrid singular type Gronwall inequality | Solutions | EXISTENCE | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | PHYSICS, FLUIDS & PLASMAS | PHYSICS, MATHEMATICAL | Differential equations | Computer simulation | Existence theorems | Mathematical analysis | Inequalities | Nonlinearity | Mathematical models

Journal Article