le Hien - Academia.edu (original) (raw)

Papers by le Hien

Research paper thumbnail of Bài giảng kinh tế vi mô

Research paper thumbnail of New finite-sum inequalities with applications to stability of discrete time-delay systems

Automatica, 2016

This paper provides new summation inequalities in both single and double forms to be used in stab... more This paper provides new summation inequalities in both single and double forms to be used in stability analysis of discrete-time systems with time-varying delays. The potential capability of the newly derived inequalities is demonstrated by establishing less conservative stability conditions for a class of linear discrete-time systems with an interval time-varying delay in the framework of linear matrix inequalities. The effectiveness and least conservativeness of the derived stability conditions are shown by academic and practical examples.

Research paper thumbnail of Exponential stability of time-delay systems via new weighted integral inequalities

Applied Mathematics and Computation, 2016

In this paper, new weighted integral inequalities (WIIs) are first derived by refining the Jensen... more In this paper, new weighted integral inequalities (WIIs) are first derived by refining the Jensen single and double inequalities. It is shown that the newly derived inequalities in this paper encompass both the Jensen inequality and its most recent improvements based on Wirtinger integral inequality. The potential capability of the proposed WIIs is demonstrated through applications in exponential stability analysis for some classes of time-delay systems in the framework of linear matrix inequalities (LMIs). The effectiveness and least conservativeness of the derived stability conditions using WIIs are shown by various numerical examples.

Research paper thumbnail of New generalized Halanay inequalities with applications to stability of nonlinear non-autonomous time-delay systems

Nonlinear Dynamics, 2015

ABSTRACT In this paper, a general class of Halanay-type non-autonomous functional differential in... more ABSTRACT In this paper, a general class of Halanay-type non-autonomous functional differential inequalities is considered. A new concept of stability, namely global generalized exponential stability, is proposed. We first prove some new generalizations of the Halanay inequality. We then derive explicit criteria for global generalized exponential stability of nonlinear non-autonomous time-delay systems based on our new generalized Halanay inequalities. Numerical examples and simulations are provided to illustrate the effectiveness of the obtained results.

Research paper thumbnail of Exponential stabilization of non-autonomous delayed neural networks via Riccati equations

Applied Mathematics and Computation, 2014

ABSTRACT This paper concerns with the problem of exponential stabilization for a class of non-aut... more ABSTRACT This paper concerns with the problem of exponential stabilization for a class of non-autonomous neural networks with mixed discrete and distributed time-varying delays. Two cases of discrete time-varying delay, namely (i) slowly time-varying; and (ii) fast time-varying, are considered. By constructing an appropriate Lyapunov–Krasovskii functional in case (i) and utilizing the Razumikhin technique in case (ii), we establish some new delay-dependent conditions for designing a memoryless state feedback controller which stabilizes the system with an exponential convergence of the resulting closed-loop system. The proposed conditions are derived through solutions of some types of Riccati differential equations. Applications to control a class of autonomous neural networks with mixed time-varying delays are also discussed in this paper. Some numerical examples are provided to illustrate the effectiveness of the obtained results.

Research paper thumbnail of Robust stabilization of linear polytopic control systems with mixed delays

Research paper thumbnail of New exponential estimate for robust stability of nonlinear neutral time-delay systems with convex polytopic uncertainties

Research paper thumbnail of Exponential stabilization for a class of hybrid systems with mixed delays in state and control

Nonlinear Analysis: Hybrid Systems, 2009

This paper proposes a switching design for the exponential stabilization problem of hybrid system... more This paper proposes a switching design for the exponential stabilization problem of hybrid systems with mixed time-delays in both the state and control. By using an improved Lyapunov-Krasovskii functional, a memoryless switching controller for the exponential stabilization of the system is designed in terms of linear matrix inequalities. The approach also allows us to compute simultaneously the two bounds that characterize the exponential stability rate of the solution.

Research paper thumbnail of A new approach to state bounding for linear time-varying systems with delay and bounded disturbances

Automatica, 2014

In this note, the problem of state bounding for linear time-varying systems with delay and bounde... more In this note, the problem of state bounding for linear time-varying systems with delay and bounded disturbances input is considered for the first time. By using a novel approach which does not involve the Lyapunov-Krasovskii functional method, new explicit delay-independent conditions are derived for the existence of a ball such that all the state trajectories of the system converge exponentially within it. A numerical example is given to illustrate the effectiveness of the obtained result.

Research paper thumbnail of Exponential stability and stabilization of a class of uncertain linear time-delay systems

Journal of the Franklin Institute, 2009

This paper provide exponential stability conditions for a class of uncertain linear hybrid time-d... more This paper provide exponential stability conditions for a class of uncertain linear hybrid time-delay systems. The system parameter uncertainties are time-varying and unknown but norm-bounded. The delay in the system states is also timevarying. By using an improved Lyapunov-Krasovskii functional, a switching rule for the exponential stability is designed in terms of the solution of Riccati-type equations. The approach allows for computation of the bounds that characterize the exponential stability rate of the solution. An application to stabilization of linear control switching systems is given. Numerical examples are given to illustrate the results.

Research paper thumbnail of Delay feedback control in exponential stabilization of linear time-varying systems with input delay

IMA Journal of Mathematical Control and Information, 2009

Abstract In this paper, we investigate the memory controller design for the exponential stabiliza... more Abstract In this paper, we investigate the memory controller design for the exponential stabilization of linear time-varying systems with control delay. Based on state transformation and an improved Lyapunov–Krasovskii functional, new sufficient conditions for the ...

Research paper thumbnail of An application of Razumikhin theorem to exponential stability for linear non-autonomous systems with time-varying delay

Applied Mathematics Letters, 2009

In this work, in the light of the Razumikhin stability theorem combined with the Newton-Leibniz f... more In this work, in the light of the Razumikhin stability theorem combined with the Newton-Leibniz formula, a new delay-dependent exponential stability condition is first derived for linear non-autonomous time delay systems without using model transformation and bounding techniques on the derivative of the time-varying delay function. The condition is presented in terms of the solution of Riccati differential equations.

Research paper thumbnail of Stability and stabilization of switched linear dynamic systems with time delay and uncertainties

Applied Mathematics and Computation, 2009

This paper considers the problem of exponential stability and stabilization of switched linear ti... more This paper considers the problem of exponential stability and stabilization of switched linear time-delay systems. The system parameter uncertainties are time-varying and unknown but norm-bounded. The delay in the system states is also time-varying. By using an improved Lyapunov-Krasovskii functional, a switching rule for the exponential stability and stabilization is designed in terms of the solution of Riccati-type equations. The approach allows for computation of the bounds that characterize the exponential stability rate of the solution. Numerical examples are given to illustrate the results.

Research paper thumbnail of Bài giảng kinh tế vi mô

Research paper thumbnail of New finite-sum inequalities with applications to stability of discrete time-delay systems

Automatica, 2016

This paper provides new summation inequalities in both single and double forms to be used in stab... more This paper provides new summation inequalities in both single and double forms to be used in stability analysis of discrete-time systems with time-varying delays. The potential capability of the newly derived inequalities is demonstrated by establishing less conservative stability conditions for a class of linear discrete-time systems with an interval time-varying delay in the framework of linear matrix inequalities. The effectiveness and least conservativeness of the derived stability conditions are shown by academic and practical examples.

Research paper thumbnail of Exponential stability of time-delay systems via new weighted integral inequalities

Applied Mathematics and Computation, 2016

In this paper, new weighted integral inequalities (WIIs) are first derived by refining the Jensen... more In this paper, new weighted integral inequalities (WIIs) are first derived by refining the Jensen single and double inequalities. It is shown that the newly derived inequalities in this paper encompass both the Jensen inequality and its most recent improvements based on Wirtinger integral inequality. The potential capability of the proposed WIIs is demonstrated through applications in exponential stability analysis for some classes of time-delay systems in the framework of linear matrix inequalities (LMIs). The effectiveness and least conservativeness of the derived stability conditions using WIIs are shown by various numerical examples.

Research paper thumbnail of New generalized Halanay inequalities with applications to stability of nonlinear non-autonomous time-delay systems

Nonlinear Dynamics, 2015

ABSTRACT In this paper, a general class of Halanay-type non-autonomous functional differential in... more ABSTRACT In this paper, a general class of Halanay-type non-autonomous functional differential inequalities is considered. A new concept of stability, namely global generalized exponential stability, is proposed. We first prove some new generalizations of the Halanay inequality. We then derive explicit criteria for global generalized exponential stability of nonlinear non-autonomous time-delay systems based on our new generalized Halanay inequalities. Numerical examples and simulations are provided to illustrate the effectiveness of the obtained results.

Research paper thumbnail of Exponential stabilization of non-autonomous delayed neural networks via Riccati equations

Applied Mathematics and Computation, 2014

ABSTRACT This paper concerns with the problem of exponential stabilization for a class of non-aut... more ABSTRACT This paper concerns with the problem of exponential stabilization for a class of non-autonomous neural networks with mixed discrete and distributed time-varying delays. Two cases of discrete time-varying delay, namely (i) slowly time-varying; and (ii) fast time-varying, are considered. By constructing an appropriate Lyapunov–Krasovskii functional in case (i) and utilizing the Razumikhin technique in case (ii), we establish some new delay-dependent conditions for designing a memoryless state feedback controller which stabilizes the system with an exponential convergence of the resulting closed-loop system. The proposed conditions are derived through solutions of some types of Riccati differential equations. Applications to control a class of autonomous neural networks with mixed time-varying delays are also discussed in this paper. Some numerical examples are provided to illustrate the effectiveness of the obtained results.

Research paper thumbnail of Robust stabilization of linear polytopic control systems with mixed delays

Research paper thumbnail of New exponential estimate for robust stability of nonlinear neutral time-delay systems with convex polytopic uncertainties

Research paper thumbnail of Exponential stabilization for a class of hybrid systems with mixed delays in state and control

Nonlinear Analysis: Hybrid Systems, 2009

This paper proposes a switching design for the exponential stabilization problem of hybrid system... more This paper proposes a switching design for the exponential stabilization problem of hybrid systems with mixed time-delays in both the state and control. By using an improved Lyapunov-Krasovskii functional, a memoryless switching controller for the exponential stabilization of the system is designed in terms of linear matrix inequalities. The approach also allows us to compute simultaneously the two bounds that characterize the exponential stability rate of the solution.

Research paper thumbnail of A new approach to state bounding for linear time-varying systems with delay and bounded disturbances

Automatica, 2014

In this note, the problem of state bounding for linear time-varying systems with delay and bounde... more In this note, the problem of state bounding for linear time-varying systems with delay and bounded disturbances input is considered for the first time. By using a novel approach which does not involve the Lyapunov-Krasovskii functional method, new explicit delay-independent conditions are derived for the existence of a ball such that all the state trajectories of the system converge exponentially within it. A numerical example is given to illustrate the effectiveness of the obtained result.

Research paper thumbnail of Exponential stability and stabilization of a class of uncertain linear time-delay systems

Journal of the Franklin Institute, 2009

This paper provide exponential stability conditions for a class of uncertain linear hybrid time-d... more This paper provide exponential stability conditions for a class of uncertain linear hybrid time-delay systems. The system parameter uncertainties are time-varying and unknown but norm-bounded. The delay in the system states is also timevarying. By using an improved Lyapunov-Krasovskii functional, a switching rule for the exponential stability is designed in terms of the solution of Riccati-type equations. The approach allows for computation of the bounds that characterize the exponential stability rate of the solution. An application to stabilization of linear control switching systems is given. Numerical examples are given to illustrate the results.

Research paper thumbnail of Delay feedback control in exponential stabilization of linear time-varying systems with input delay

IMA Journal of Mathematical Control and Information, 2009

Abstract In this paper, we investigate the memory controller design for the exponential stabiliza... more Abstract In this paper, we investigate the memory controller design for the exponential stabilization of linear time-varying systems with control delay. Based on state transformation and an improved Lyapunov–Krasovskii functional, new sufficient conditions for the ...

Research paper thumbnail of An application of Razumikhin theorem to exponential stability for linear non-autonomous systems with time-varying delay

Applied Mathematics Letters, 2009

In this work, in the light of the Razumikhin stability theorem combined with the Newton-Leibniz f... more In this work, in the light of the Razumikhin stability theorem combined with the Newton-Leibniz formula, a new delay-dependent exponential stability condition is first derived for linear non-autonomous time delay systems without using model transformation and bounding techniques on the derivative of the time-varying delay function. The condition is presented in terms of the solution of Riccati differential equations.

Research paper thumbnail of Stability and stabilization of switched linear dynamic systems with time delay and uncertainties

Applied Mathematics and Computation, 2009

This paper considers the problem of exponential stability and stabilization of switched linear ti... more This paper considers the problem of exponential stability and stabilization of switched linear time-delay systems. The system parameter uncertainties are time-varying and unknown but norm-bounded. The delay in the system states is also time-varying. By using an improved Lyapunov-Krasovskii functional, a switching rule for the exponential stability and stabilization is designed in terms of the solution of Riccati-type equations. The approach allows for computation of the bounds that characterize the exponential stability rate of the solution. Numerical examples are given to illustrate the results.