Ngoc Pham

• Professor at Vietnam National University Ho Chi Minh City

This paper addresses the exponential stability of nonlinear delay differential equations with Markovian switching. Drawing upon the comparison principle, we introduce the explicit criteria for achieving the exponential stability in mean square (sense). These criteria are formulated in terms of the equation coefficients and the generator of the Mark...

We present a novel approach to the exponential stability of switched functional differential equations. Our approach does not involve Lyapunov functions. It is simple and based upon spectral properties of Metzler matrices, a comparison principle and the average dwell-time technique. Consequently, some new explicit criteria for the exponential stabi...

This paper is concerned with exponential contraction and expansion of regime switching diffusions. The focus is on the behavior of the distance from a solution to another solution, rather than with respect to some equilibrium point. The moment and almost sure exponential contraction and expansion are investigated. Sufficient conditions for moment a...

This paper focuses on exponential stability of numerical solutions of neutral stochastic delay differential equations. A novel approach is introduced to study numerical approximation methods of neutral stochastic differential equations with time‐dependent delay. In contrast to the advances in the literature, this work provides a new method and new...

This paper addresses exponential stability of a class of stochastic delay differential equations and their numerical solutions. We begin by establishing criteria for exponential stability in mean square of stochastic delay differential equations. We then show that the Euler–Maruyama approximation method correctly reproduces exponential stability in...

By a novel approach, we present some new criteria for the exponential stability in mean square of solutions of non-linear stochastic difference systems with time-varying delays. A discussion of the obtained results is given. Illustrative examples and simulations are provided.

By a novel approach, we present in this paper for the first time, some explicit criteria for the exponential stability in mean square of solutions of general stochastic difference systems with time-varying delays. Both delay-independent and delay-dependent stability criteria are provided. A discussion and illustrative examples are given.

By a novel approach, we present in this paper for the first time, some explicit criteria for the contraction in mean square of solutions of general stochastic difference systems with time-varying delays. Illustrative examples are given.

4th International Conference on Pure and Applied Mathematics (ICPAM-VAN 2022) VAN, TURKEY Dear Colleague, Due to the global spread of COVID-19, we organize a virtual conference entitled 4th International Conference on Pure and Applied Mathematics (ICPAM-VAN 2022), which will be held on June 22-23, 2022. For more information, you can http://icpam.yy...

General neutral stochastic functional differential equations are considered. A novel approach to exponential stability of such equations is proposed. New criteria for the mean square exponential stability of neutral stochastic functional differential equations are given. A discussion and illustrative examples are presented.

This work addresses the exponential stability in mean square of general neutral stochastic differential equations with delays. A simple approach to the exponential stability of the neutral stochastic differential equations with delays is proposed. Novel criteria for the exponential stability in mean square of such equations are presented. A compari...

By a new approach, we get some new scalar criteria for the exponential stability of general nonlinear Volterra integro-differential equations. Then applications to models of biological population growth and Cohen-Grossberg neural networks are presented.

Stochastic functional differential equations with infinite delay are considered. A novel approach to exponential stability of such equations is proposed. New criteria for the mean square exponential stability of general stochastic functional differential equations with infinite delay are presented. Illustrative examples are given.

Using a novel approach, we present some new scalar criteria for the uniform asymptotic stability of general nonlinear Volterra integro-differential equations. Discussion and illustrative examples of the obtained results are given.

General non-linear functional differential equations are considered. New explicit criteria for the exponential stability are presented. The stability criteria given in this paper include many existing results as particular cases. In particular, they unify, generalise and improve some ones published recently in [Ngoc, P. H. A. (2012). On exponential...

General nonlinear Volterra integro-differential equations are considered. Explicit criteria for uniform asymptotic stability and exponential stability of such equations are given. Applications to models of growth of biological populations and of grazing systems are presented.

General nonlinear difference equations with time‐varying delays are considered. Explicit criteria for contraction of such equations are presented. Then some simple sufficient conditions for global exponential stability of equilibria and for stability of invariant sets are derived. Furthermore, explicit criteria for existence, uniqueness and global...

Using a novel approach, we present some new explicit criteria for the uniform asymptotic stability and the exponential stability of nonlinear Volterra integro-differential equations. Some examples are given to illustrate the obtained results.

Using a novel approach, we present some new explicit criteria for global exponential stability of the zero solution of general nonlinear time-varying Volterra difference equations. Furthermore, an explicit stability bound for equations subject to nonlinear time-varying perturbations is given. Finally, the obtained results are used to study uniform...

General linear non-autonomous functional differential equations of neutral type are considered. A novel approach to exponential stability of neutral functional differential equations is presented. Consequently, explicit criteria are derived for exponential stability of linear non-autonomous functional differential equations of neutral type. A brief...

We present a novel approach to exponential stability of functional differential systems. Our approach is relied upon the theory of positive linear functional differential systems and a comparison principle. Consequently, we get some comparison tests and explicit criteria for exponential stability of functional differential systems. Two examples are...

General non-linear differential systems with time-varying delays are considered. Explicit criteria for existence, uniqueness and global exponential stability of periodic solutions are given. Then the obtained result is used to investigate exponential stability of periodic solutions of delayed neural networks.

By a novel approach, we get explicit robust stability bounds for positive linear time-invariant time delay differential systems subject to time-varying structured perturbations or non-linear time-varying perturbations. Some examples are given to illustrate the obtained results. To the best of our knowledge, the results of this paper are new.

Time-varying differential systems with infinite delay are considered. Explicit criteria for global exponential stability of linear (nonlinear) systems are presented. Furthermore, an explicit robust stability bound for linear systems subject to time-varying perturbations is given. The exponential stability criteria for nonlinear systems are used to...

General nonlinear time-varying differential systems with delay are considered. Several new explicit criteria for exponential stability are given. A discussion of the obtained results and two illustrative examples are presented. © 2015, American Institute of Mathematical Sciences. All rights reserved.

Using a novel approach, we present some new explicit criteria for global exponential stability of the zero solution of general nonlinear Volterra difference equations in phase spaces. In particular, this gives a solution to an open problem posed very recently by E. Braverman and I. M. Karabash in Journal of Difference Equations and Applications 18,...

General nonlinear differential systems with time-varying delay are considered. Several explicit criteria for global exponential stability are presented. Two examples are given to illustrate the obtained results.

Linear time-varying delay difference equations with continuous time are considered. New criteria for exponential stability are given. Furthermore, an explicit stability bound for equations subject to time-varying perturbations is presented. Some examples are given to illustrate the obtained results.

General linear functional differential equations with infinite delay are considered. We first give an explicit criterion for positivity of the solution semigroup of linear functional differential equations with infinite delay and then a Perron-Frobenius type theorem for positive equations. Next, a novel criterion for the exponential asymptotic stab...

By a novel approach, we get explicit robust stability bounds for positive linear differential systems subject to time-varying multi-perturbations and time-varying affine perturbations. Our approach is based on the celebrated Perron-Frobenius theorem and ideas of the comparison principle. An example is given to illustrate the obtained results.

General nonlinear time-varying differential systems are considered. An explicit criterion for exponential stability is presented. Furthermore, an explicit robust stability bound for systems subjected to nonlinear time-varying perturbations is given. In particular, it is shown that the generalized Aizerman conjecture holds for positive linear system...

General nonlinear Volterra difference equations with infinite delay are considered. A new explicit criterion for global exponential stability is given. Furthermore, we present a stability bound for equations subject to nonlinear perturbations. Two examples are given to illustrate the results obtained.

General linear time-varying differential systems with delay are considered. Several explicit criteria for exponential stability are presented. Furthermore, an explicit robust stability bound for systems subject to time-varying perturbations is given. Two examples are given to illustrate the obtained results. To the best of our knowledge, the result...

We first give explicit criteria for exponential stability of general linear nonautonomous functional differential equations. Then the obtained results are extended to nonlinear functional differential equations. Two examples are given to illustrate the results. To the best of our knowledge, the results of this note are new.

General nonlinear time-varying difference systems with time-varying delay are considered. Some new explicit criteria for global exponential stability are given. Two examples are given to illustrate the obtained results.

We first prove an explicit criterion for positive linear time-varying differential systems with distributed delay. Then some simple criteria for exponential stability of positive linear time-invariant differential systems with delay are presented. Finally, we extend obtained results to linear differential systems with time-varying delay and to nonl...

We give some explicit stability bounds for discrete-time systems subjected to time-varying and nonlinear perturbations. The obtained results are extensions of some well-known results in (Hinrichsen and Son in Int. J. Robust Nonlinear Control 8:1169-1188, 1998; Shafai et al. in IEEE Trans. Autom. Control 42:265-270, 1997) to nonlinear time-varying p...

General nonlinear differential systems with time-varying delays are considered. Several explicit criteria for exponential stability are presented. An example is given to illustrate the obtained results. To the best of our knowledge, the results of this note are new.

Linear Volterra integro-differential equations with infinite delay are studied. Sufficient conditions for exponential asymptotic stability of linear time-varying equations with delay are given. Then several explicit criteria for exponential asymptotic stability of linear time-invariant equations are presented. Two examples are given to illustrate t...

We study positive linear Volterra integro-differential systems with infinitely many delays. Positivity is characterized in terms of the system entries. A generalized version of the Perron–Frobenius theorem is shown; this may be interesting in its own right but is exploited here for stability results: explicit spectral criteria for L1-stability and...

We give an explicit criterion for positivity of the solution semigroup of linear differential equations with infinite delay and a Perron–Frobenius type theorem for positive equations. Furthermore, a novel criterion for the exponential asymptotic stability of positive equations is presented. Finally, we provide a sufficient condition for the exponen...

Linear Volterra-Stieltjes differential equations are considered. We give a sufficient condition which ensures that the uniform asymptotic stability and the exponential asymptotic stability of linear Volterra-Stieltjes differential equations coincide. In particular, this yields necessary and sufficient conditions for the exponential asymptotic stabi...

We study positive linear Volterra integro-differential equations in Banach lattices. A characterization of positive equations is given. Furthermore, an explicit spectral criterion for uniformly asymptotic stability of positive equations is presented. Finally, we deal with problems of robust stability of positive systems under structured perturbatio...

Linear time-varying Volterra integro-differential equations of non-convolution type are considered. Positivity is characterized and a sufficient condition for exponential asymptotic stability is presented.

An explicit criterion for positive linear Volterra-Stieltjes differential systems is given. Then new explicit criteria for uniform asymptotic stability and exponential asymptotic stability of positive linear Volterra-Stieltjes differential systems are presented. Finally, a crucial difference between the uniform asymptotic stability and the exponent...

We first introduce the notion of positive linear Volterra-Stieltjes differential systems. Then, we give some characterizations of positive systems. An explicit criterion and a Perron-Frobenius type theorem for positive linear Volterra-Stieltjes differential systems are given. Next, we offer a new criterion for uniformly asymptotic stability of posi...

We first introduce a class of positive linear Volterra difference equations. Then, we offer explicit criteria for uniform asymptotic stability of positive equations. Furthermore, we get a new Perron-Frobenius theorem for positive linear Volterra difference equations. Finally, we study robust stability of positive equations under structured perturba...

An explicit criterion for positivity of the solution semigroup of linear Volterra integro-differential systems with infinitely many delays is given. Then exponential asymptotic stability is studied, and it is shown that, roughly speaking, a linear Volterra integro-differential system with delay is exponentially asymptotically stable if its characte...

We give Lyapunov exponents of solutions to linear differential equations of the form x'=Ax+f(t), where A is a complex matrix and f(t) is a [tau]-periodic continuous function. Notice that f(t) is not "small" as t-->[infinity]. The proof is essentially based on a representation [J. Kato, T. Naito, J.S. Shin, A characterization of solutions in linear...

We give new representations of solutions for the periodic linear difference equation of the type $x(n+1)=B(n)x(n)+b(n)$, where complex nonsingular matrices $B(n)$ and vectors $b(n)$ are $\rho$-periodic. These are based on the Floquet multipliers and the Floquet exponents, respectively. By using these representations, asymptotic behavior of solution...

We first introduce the notion of positive linear Volterra integrodifferential equations. Then we give some characterizations of these positive equations. An explicit criterion and a Perron-Frobenius-type theorem for positive linear Volterra integrodifferential equations are given. Then we offer a new criterion for uniformly asymptotic stability of...

We study stability radii of linear Volterra–Stieltjes equations under multi-perturbations and affine perturbations. A lower and upper bound for the complex stability radius with respect to multi-perturbations are given. Furthermore, in some special cases concerning the structure matrices, the complex stability radius can precisely be computed via t...

We first give a sufficient condition for positivity of the solution semigroup of linear functional difference equations. Then, we obtain a Perron–Frobenius theorem for positive linear functional difference equations. Next, we offer a new explicit criterion for exponential stability of a wide class of positive equations. Finally, we study stability...

We first introduce the notion of positive linear Volterra integral equations. Then, we offer a criterion for positive equations in terms of the resolvent. In particular, equations with nonnegative kernels are positive. Next, we obtain a variant of the Paley–Wiener theorem for equations of this class and its extension to perturbed equations. Further...

In this paper, we first prove that if a linear neutral functional differential equation is positive then it must degrade into a linear functional differential equation of retarded type. Then, we give some explicit criteria for positive linear functional differential equations. Consequently, we obtain a novel criterion for exponential stability of p...

We first give a criterion for positivity of the solution semigroup of linear Volterra integro-differential systems. Then, we offer some explicit conditions under which the solution of a positive linear Volterra system is exponentially stable or (robustly) lies in L2[0,+∞).

We study stability radii of higher order linear difference systems under multi-perturbations. A formula for complex stability radius of higher order linear difference systems under multi-perturbations is given. Then, for the class of positive systems, we prove that the complex stability radius and real stability radius of the system under multi-per...

We deal with problems of maximizing the norm of the transfer matrix function of linear dynamical systems. It is shown that if a linear system is positive and (exponentially) asymptotically stable then the norm of its transfer matrix function attains the maximum at a specific point on the boundary of the stable region. For sake of space, exposure is...

In this paper, we give a characterization of spectral abscissa of positive linear functional differential equations. Then the obtained result is applied to derive necessary and sufficient conditions for the exponential stability of positive linear functional differential equations. Finally, we give an extension of the classical Perron–Frobenius the...

In this work, we give an extension of the classical Perron–Frobenius theorem to positive quasi-polynomial matrices. Then the result obtained is applied to derive necessary and sufficient conditions for the exponential stability of positive linear time-delay differential systems.

We study robustness of -stability of linear difference equations under multiperturbation and affine perturbation of coefficient matrices via the concept of -stability radius. Some explicit formulae are derived for these -stability radii. The obtained results include the corresponding ones established earlier in Hinrichsen and Son and Ngoc and Son a...

In this paper, we present a unifying approach to the problems of computing of stability radii of positive linear systems. First, we study stability radii of linear time-invariant parameter-varying differential systems. A formula for the complex stability radius under multi perturbations is given. Then, under hypotheses of positivity of the system m...

In this paper, we give some sufficient conditions for exponential stability of linear neutral functional differential equations. The obtained results are extensions of the recent results in [D.Q. Cao, P. He, Stability criteria of linear neutral systems with a single delay, Appl. Math. Comput. 148 (2004) 135–143, D.Q. Cao, P. He, Sufficient conditio...

We give a new characterization of exponential dichotomy of linear difference equations in terms of -admissibility. The obtained result is a discrete version of the recent new result of Preda et al. [(L ,L )-admissibility and exponential dichotomy of evolution processes on the half-plane, Integral Equations Operator Theory, 49 (2004), 405–418] on ex...

In this paper, we study robustness of the strong delay-independent stability of linear time-delay systems under multi-perturbation and affine perturbation of coefficient matrices via the concept of strong delay-independent stability radius (shortly, strong stability radius). We prove that for class of positive time-delay systems, complex and real s...

We study stability radii of linear retarded systems described by general linear functional differential equations. A lower and an upper bound for the complex stability radius with respect to multi-perturbations are given. Furthermore, in some special cases concerning the structure matrices, the complex stability radius can precisely be computed via...

In this paper, we study stability radii of linear systems under multi-perturbation of the coefficient matrices. Formulas for complex stability radius are derived. We then consider linear positive systems and prove that for this class of systems, the complex stability radius is equal to the real stability radius which can be computed via a simple fo...

In this paper, we give an extension of the classical Perron–Frobenius the-orem to positive polynomial matrices. Then the obtained result is applied to de-rive necessary and sufficient conditions for the exponential stability of positive linear discrete-time systems.

In this paper we study stability radii of positive polynomial matrices under affine perturbations of the coefficient matrices. It is shown that the real and complex stability radii coincide. Moreover, explicit formulas are derived for these stability radii and illustrated by some examples.

In this paper we study stability radii of positive linear difference equations under arbitrary affine parameter perturbations. It is shown that real and complex stability radii of positive equations coincide for block-diagonal disturbances. Moreover, for these stability radii, estimates and computable formulae are derived which generalize to positi...

We study robust stability of linear time delay systems under structured parameter uncertainty. A formula for complex stability radius is derived. We then consider linear positive delay systems and prove that for this class of systems the complex stability radius is equal to the real stability radius which can be computed via a simple formula. An il...

In this paper we study robust stability of positive linear time-delay systems under arbitrary affine parameter perturbations. It is shown that real and complex stability radii of positive systems coincide for block-diagonal disturbances. Moreover, for these stability radii, estimates and computable formulae are derived which generalize to positive...

We study robustness of Testability of linear difference equations under multi-perturbation and affine perturbation of coefficient matrices via the concept of DInstability radius. Some explicit formulae are derived for these D-stability radii. The obtained results include the corresponding ones established earlier in [3], [4], [9], [10] as particula...

Abstract

We study positive linear Volterra integro-difierential systems with inflnitely many delays. Positivity is characterized in terms of the system en- tries. A generalized version of the Perron-Frobenius Theorem is shown; this may be interesting in its own right but is exploited here for stability results: explicit spectral criteria for L1-stability an...