Vu Ngoc Phat

Exponential Stabilization of Neural Networks With Various Activation Functions and Mixed Time-Varying Delays

This paper presents some results on the global exponential stabilization for neural networks with various activation functions and time-varying continuously distributed delays. Based on augmented time-varying Lyapunov-Krasovskii functionals, new delay-dependent conditions for the global exponential stabilization are obtained in terms of linear matrix inequalities. A numerical example is given to illustrate the feasibility of our results.

Robust stability and stabilizability of uncertain linear hybrid systems with state delays

In this brief, we consider a class of uncertain linear discrete-time switched systems with state delays. By solving certain matrix and Riccati-like inequalities, sufficient conditions for the robust stability and stabilizability of the system are given.

Robust stabilization of linear uncertain discrete-time systems via a limited capacity communication channel

Abstract The paper considers the problem of robust stabilization of linear uncertain discrete-time systems via limited capacity communication channels. We consider the case when the control input is to be transmitted via communication channel with a bit-rate constraint. A constructive method to design a robustly stabilizing controller is proposed.

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

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.

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

Abstract This paper presents new exponential stability and stabilization conditions for a class of uncertain linear time-delay systems. The unknown norm-bounded uncertainties and the delays are time-varying. Based on an improved Lyapunov–Krasovskii functional combined with Leibniz–Newton formula, the robust stability conditions are derived in terms of linear matrix inequalities (LMIs), which allows to compute simultaneously the two bounds that characterize the exponential stability rate of the solution. The result can be extended to uncertain systems with time-varying multiple delays. The effectiveness of the two stability bounds and the reduced conservatism of the conditions are shown by numerical examples.

Switched controller design for stabilization of nonlinear hybrid systems with time-varying delays in state and control

Abstract This paper deals with the problem of stabilization for a class of hybrid systems with time-varying delays. The system to be considered is with nonlinear perturbation and the delay is time varying in both the state and control. Using an improved Lyapunov–Krasovskii functional combined with Newton–Leibniz formula, a memoryless switched controller design for exponential stabilization of switched systems is proposed. The conditions for the exponential stabilization are presented in terms of the solution of matrix Riccati equations, which allow for an arbitrary prescribed stability degree.

Novel criteria for finite-time stabilization and guaranteed cost control of delayed neural networks

In this paper, the problem of robust finite-time stabilization with guaranteed cost control for a class of delayed neural networks is considered. The time delay is a continuous function belonging to a given interval, but not necessary to be differentiable. We develop a general framework for finite-time stabilization with guaranteed cost control based on the Lyapunov functional method and new generalized Jensen integral inequality. Novel criteria for the existence of guaranteed cost controllers are established in terms of linear matrix inequalities (LMIs). The proposed conditions allow us to design the state feedback controllers which robustly stabilize the closed-loop system in the finite time. A numerical example is given to illustrate the efficiency of the proposed method.

Delay-dependent exponential stabilization for uncertain linear systems with interval non-differentiable time-varying delays

Abstract In this paper, the problem of exponential stabilization for a class of linear systems with time-varying delay is studied. The time delay is a continuous function belonging to a given interval, which means that the lower and upper bounds for the time-varying delay are available, but the delay function is not necessary to be differentiable. Based on the construction of improved Lyapunov–Krasovskii functionals combined with Leibniz–Newton’s formula, new delay-dependent sufficient conditions for the exponential stabilization of the systems are first established in terms of LMIs. Numerical examples are given to demonstrate that the derived conditions are much less conservative than those given in the literature.

Exponential stability and stabilization of uncertain linear time-varying systems using parameter dependent Lyapunov function

In this paper, the problem of exponential stability and stabilization for a class of uncertain linear time-varying systems is considered. The system matrix belongs to a polytope and the time-varying parameter as well as its time derivative are bounded. Based on a time-varying version of Lyapunov stability theorem, new sufficient conditions for the exponential stability and stabilization via parameter dependent state feedback controllers (i.e., a gain scheduling controllers) are given. Using parameter dependent Lyapunov function, the conditions are formulated in terms of two linear matrix inequalities without introducing extra useless decision variables and hence are simply verified. The results are illustrated by numerical examples.

Constrained Control Problems of Discrete Processes

Introduction and motivation foundation linear controllability nonlinear controllability applications and related topics conclusions.