Piyapong Niamsup

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.

Adaptive control and synchronization of the perturbed Chua's system

In this paper, we study perturbed Chuas system. First, we study the stability of equilibrium points of perturbed Chuas system. Then, we control the chaotic behavior of perturbed Chuas system to its equilibrium points using linear feedback control and adaptive control methods. Finally, we study chaos synchronization of perturbed Chuas system by using active control and adaptive control methods.

Improved exponential stability for time-varying systems with nonlinear delayed perturbations

In this paper, a new sufficient delay dependent exponential stability condition for a class of linear time-varying systems with nonlinear delayed perturbations is derived by using an improved Lyapunov–Krasovskii functional. The proposed exponential stability conditions are formulated in terms of the solution of Lyapunov differential equations. The approach allows for computation of the bounds that characterize the exponential stability rate of convergence of the solution. Compared with existing results, our conditions are shown to be less conservative. Numerical examples are given to illustrate the effectiveness of the obtained conditions.

New discrete type inequalities and global stability of nonlinear difference equations

In this work, we introduce discrete type inequalities. On the basis of these inequalities, we derive new global stability conditions for nonlinear difference equations.

Robust exponential stability and stabilizability of linear parameter dependent systems with delays

Abstract The robust exponential stability and stabilizability problems are addressed in this paper for a class of linear parameter dependent systems with interval time-varying and constant delays. In this paper, restrictions on the derivative of the time-varying delay is not required which allows the time-delay to be a fast time-varying function. Based on the Lyapunov–Krasovskii theory, we derive delay-dependent exponential stability and stabilizability conditions in terms of linear matrix inequalities (LMIs) which can be solved by various available algorithms. Numerical examples are given to illustrate the effectiveness of our theoretical results.

New Results on Robust Stability and Stabilization of Linear Discrete-Time Stochastic Systems with Convex Polytopic Uncertainties

This paper addresses the robust stability for a class of linear discrete-time stochastic systems with convex polytopic uncertainties. The system to be considered is subject to both interval time-varying delays and convex polytopic type uncertainties. Based on the augmented parameter-dependent Lyapunov-Krasovskii functional, new delay-dependent conditions for the robust stability are established in terms of linear matrix inequalities. An application to robust stabilization of linear discrete-time stochastic control systems is given. Numerical examples are included to illustrate the effectiveness of our results.

A switching rule for exponential stability of switched recurrent neural networks with interval time-varying delay

This paper studies the problem for exponential stability of switched recurrent neural networks with interval time-varying delay. The time delay is a continuous function belonging to a given interval, but not necessarily differentiable. By constructing a set of argumented Lyapunov-Krasovskii functionals combined with the Newton-Leibniz formula, a switching rule for exponential stability of switched recurrent neural networks with interval time-varying delay is designed via linear matrix inequalities, and new sufficient conditions for the exponential stability of switched recurrent neural networks with interval time-varying delay via linear matrix inequalities (LMIs) are derived. A numerical example is given to illustrate the effectiveness of the obtained result.

A new result on finite-time control of singular linear time-delay systems

Abstract In this paper, problem of robust finite-time stability and control is first time discussed for singular linear time-delay systems subject to disturbance. By developing delay singular value decomposition approach combining with linear matrix inequality (LMI) technique, new sufficient conditions for the existence of such controllers are proposed in terms of the solvability to a set of LMIs. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

Finite-time stability of singular nonlinear switched time-delay systems: A singular value decomposition approach

Abstract In this paper, a constructive geometric design of switching laws is proposed for the finite-time stability of singular nonlinear switched systems subjected to delay and disturbance. The state-dependent switching law is constructed based on the construction of a partition of the stability state regions in convex cones such that each system mode is activated in one particular conic zone. Using the state-space singular value decomposition approach, new delay-dependent sufficient conditions for the finite-time stability of the system are presented in terms of linear matrix inequalities (LMIs). The obtained results are applied to uncertain linear singular switched systems with delay. Numerical examples are given to illustrate the effectiveness of the proposed method.