Kanit Mukdasai

Robust Exponential Stability for LPD Discrete-Time System with Interval Time-Varying Delay

This paper investigates the problem of robust exponential stability for uncertain linear-parameter dependent (LPD) discrete-time system with delay. The delay is of an interval type, which means that both lower and upper bounds for the time-varying delay are available. The uncertainty under consideration is norm-bounded uncertainty. Based on combination of the linear matrix inequality (LMI) technique and the use of suitable Lyapunov-Krasovskii functional, new sufficient conditions for the robust exponential stability are obtained in terms of LMI. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.

New Robust Exponential Stability Criterion for Uncertain Neutral Systems with Discrete and Distributed Time-Varying Delays and Nonlinear Perturbations

We investigate the problem of robust exponential stability for uncertain neutral systems with discrete and distributed time-varying delays and nonlinear perturbations. Based on the combination of descriptor model transformation, decomposition technique of coefficient matrix, and utilization of zero equation and new Lyapunov functional, sufficient conditions for robust exponential stability are obtained and formulated in terms of linear matrix inequalities (LMIs). The new stability conditions are less conservative and more general than some existing results.

New Delay-Dependent Robust Exponential Stability Criteria of LPD Neutral Systems with Mixed Time-Varying Delays and Nonlinear Perturbations

This paper is concerned with the problem of robust exponential stability for linear parameter-dependent (LPD) neutral systems with mixed time-varying delays and nonlinear perturbations. Based on a new parameter-dependent Lyapunov-Krasovskii functional, Leibniz-Newton formula, decomposition technique of coefficient matrix, free-weighting matrices, Cauchy’s inequality, modified version of Jensen’s inequality, model transformation, and linear matrix inequality technique, new delay-dependent robust exponential stability criteria are established in terms of linear matrix inequalities (LMIs). Numerical examples are given to show the effectiveness and less conservativeness of the proposed methods.

An LMI approach to stability for linear time-varying system with nonlinear perturbation on time scales

We consider Lyapunov stability theory of linear time-varying system and derive sufficient conditions for uniform stability, uniform exponential stability, 𝜓-uniform stability, and h-stability for linear time-varying system with nonlinear perturbation on time scales. We construct appropriate Lyapunov functions and derive several stability conditions. Numerical examples are presented to illustrate the effectiveness of the theoretical results.

New Delay-Dependent Robust Stability Criterion for LPD Discrete-Time Systems with Interval Time-Varying Delays

This paper investigates the problem of robust stability for linear parameter-dependent (LPD) discrete-time systems with interval time-varying delays. Based on the combination of model transformation, utilization of zero equation, and parameter-dependent Lyapunov-Krasovskii functional, new delay-dependent robust stability conditions are obtained and formulated in terms of linear matrix inequalities (LMIs). Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.

Delay-Dependent Robust Performance for Uncertain Neutral Systems with Mixed Time-Varying Delays and Nonlinear Perturbations

This paper deals with the problems of delay-dependent stability and performance for uncertain neutral systems with time-varying delays, and nonlinear perturbations. The time-varying delays are neutral, discrete, and distributed time-varying delays that the upper bounds for the delays are available. The restrictions on the derivatives of the discrete and distributed time-varying delays are removed, which mean that a fast discrete time-varying delay is allowed. The uncertainties under consideration are nonlinear time-varying parameter perturbations and norm-bounded uncertainties, respectively. Firstly, by applying a novel Lyapunov-Krasovskii functional approach, Wirtinger-based integral inequality, Peng-Park’s integral inequality, decomposition technique of constant matrix, descriptor model transformation, Leibniz Newton formula and utilization of zero equation, and improved delay-dependent bounded real lemmas (BRL) for systems are established in terms of linear matrix inequalities (LMIs). Then, based on the obtained BRL, some less conservative delay-dependent stability criteria of uncertain neutral systems with mixed time-varying delays and nonlinear perturbations are obtained and improved performance criterion with the framework of LMIs is introduced. Finally, some numerical examples are given to illustrate that the presented method is effective.

On robust stability for uncertain neutral systems with non-differentiable interval time-varying discrete delay and nonlinear perturbations

In this paper, we investigate the problem of delay-range-dependent robust stability analysis for uncertain neutral systems with interval time-varying delays and nonlinear perturbations. The restriction on the derivative of the discrete interval time-varying delay is removed. By applying the augmented Lyapunov–Krasovskii functional approach, new improved integral inequalities, descriptor model transformation, Leibniz–Newton formula and utilization of zero equation, new delay-range-dependent robust stability criteria are derived in terms of linear matrix inequalities (LMIs) for the considered systems. Numerical examples have shown to illustrate the significant improvement on the conservatism of the delay upper bound over some reported results.

Global synchronization for hybrid coupled neural networks with interval time-varying delays: A matrix-based quadratic convex approach

This paper is concerned with the global synchronization problems for coupled neural networks (NNs) with hybrid coupling and interval time-varying delays. An appropriate Lyapunov–Krasovskii functional (LKF) and Kronecker product properties are used to form some new delay-dependent synchronization conditions in terms of linear matrix inequalities. A matrix-based quadratic convex approach introduce for sufficient conditions to ensure global synchronization where the time-varying delay is continuous uniformly bounded and its time-derivative bounded by upper and lower bounds. Simulation results are given to show the effectiveness and benefits of the proposed methods.

New Delay-Range-Dependent Robust Exponential Stability Criteria of Uncertain Impulsive Switched Linear Systems with Mixed Interval Nondifferentiable Time-Varying Delays and Nonlinear Perturbations

We investigate the problem of robust exponential stability analysis for uncertain impulsive switched linear systems with time-varying delays and nonlinear perturbations. The time delays are continuous functions belonging to the given interval delays, which mean that the lower and upper bounds for the time-varying delays are available, but the delay functions are not necessary to be differentiable. The uncertainties under consideration are nonlinear time-varying parameter uncertainties and norm-bounded uncertainties, respectively. Based on the combination of mixed model transformation, Halanay inequality, utilization of zero equations, decomposition technique of coefficient matrices, and a common Lyapunov functional, new delay-range-dependent robust exponential stability criteria are established for the systems in terms of linear matrix inequalities (LMIs). A numerical example is presented to illustrate the effectiveness of the proposed method.