Sufficient Delay-dependent Stability Conditions Research Articles

Adaptive dynamic programming-based optimal regulation on input-constrained nonlinear time-delay systems

The adaptive dynamic programming (ADP)-based optimal regulation strategy is put forward for input-constrained nonlinear time-delay systems. In the spirit of Lyapunov theories, the stability of the nominal system is investigated in terms of linear matrix inequalities (LMIs), which consequently gives rise to sufficient delay-dependent stability conditions. Afterward, a single neural network (NN) which serves as critic and actor NN simultaneously is employed for the realization of ADP-based optimal regulation. The NN weights are updated in real-time and the weight estimate errors are proved to be convergent. As a result, computational complexity is efficiently decreased together with the storage space. Numerical simulation shows the validation of our approach.Kindly check and confirm the inserted city name is correct. Amend if necessary.CorrectKindly check and confirm the Organization division and Organization name of Affiliation 2.Correcy

<i>H</i><SUB align="right">∞ control of asynchronous networked control systems with Markov time delays

In this paper, the solutions to the H∞ synthesis problems of stochastic asynchronous discrete-time (DT) networked control systems (NCSs) with random communication time delays are proposed according to the following steps. Firstly, a new Lyapunov-Krasovskii functional is explicitly constructed to analyse the stochastic stability of the systems. Both sensor-to-controller (S-C) and controller-to-actuator (C-A) random networked-induced delays, which are two Markov chains, are considered in the analysis. Moreover, the stochastic sampling of S-C and holding of C-A are also considered in the analysis. Secondly, based on a specified definition of the state with delay and a more rigorous inequality, sufficient delay-dependent stability conditions can be transformed into the form of linear matrix inequalities (LMIs), the LMIs can be conveniently solved by LMI tools. Finally, the proposed theory is validated by a simulation example.

Delay-dependent stability of numerical methods for delay differential systems of neutral type

We are concerned with stability of numerical methods for delay differential systems of neutral type. In particular, delay-dependent stability of numerical methods is investigated. By means of the H-matrix norm, a necessary and sufficient condition for the asymptotic stability of analytic solution of linear neutral differential systems is derived. Then, based on the argument principle, sufficient conditions for delay-dependent stability of Runge–Kutta and linear multi-step methods are presented, respectively. Furthermore, two algorithms are provided for checking delay-dependent stability of analytical and numerical solutions, respectively. Numerical examples are given to illustrate the main results.

New stability conditions for GRNs with neutral delay

In this paper, the asymptotic stability problem of genetic regulatory networks with time-varying/constant neutral delay is considered. By introducing a new Lyapunov---Krasovskii functional and applying the free weighting matrix technique, sufficient delay-dependent stability conditions are developed and presented in terms of strict linear matrix inequality, which can be easily verified by using the LMI toolbox. Finally, two numerical examples are provided to demonstrate the effectiveness and reduced conservativeness of the proposed algorithm.

Exponential Stability of Integral Delay Systems With a Class of Analytic Kernels

The exponential stability of a class of integral delay systems with analytic kernels is investigated by using the Lyapunov-Krasovskii functional approach. Sufficient delay-dependent stability conditions and exponential estimates for the solutions are derived. Special attention is paid to the particular cases of polynomial and exponential kernels.

On stability of integral delay systems

The exponential stability of a class of integral delay systems is investigated by using the Lyapunov–Krasovskii functional approach. Sufficient delay-dependent stability conditions and exponential estimates for the solutions are derived.

Delay Dependent Robust Exponential Stability Criterion for Perturbed and Uncertain Neutral Systems with Time Varying Delays

This paper deals with the issue of robust exponential stability of uncertain neutral system with time varying delay and nonlinear perturbations. Using Lyapunov-Krasovskii functional, new sufficient delay dependent stability conditions have been derived in terms of Linear Matrix Inequalities LMIs solved using efficient convex optimization algorithms. Neither model transformation, nor estimating techniques for cross terms, nor free weighting matrices are involved in this work. Numerical examples are considered to show the efficiency of the proposed stability approach.

Memory state feedback controller design for singular systems with multiple internal constant point delays

The problem of delay-dependent stabilisation for singular linear continuous-time systems with multiple internal incommensurate constant point delays is investigated. The condition when a singular system subject to point delays is regular independent of time delays is given and it can be easily tested with numerical or algebraic methods. Based on the Lyapunov-Krasovskii functional approach and the descriptor integral-inequality lemma, a sufficient condition for delay-dependent stability is obtained. The main idea is to design multiple memory state feedback control laws such that the resulting closed-loop system is regular independent of time delays, impulse free and stable via solving matrix inequality problem. An explicit expression for the desired memory state feedback control law is also given. Finally, a numerical example is presented to illustrate the effectiveness and the availability for the proposed method.

On the Exponential Stability of a Class of Integral Delay Systems

Abstract The exponential stability of a class of integral delay systems is investigated by using the Lyapunov-Krasovskii functional approach. Sufficient delay-dependent stability conditions and exponential estimates for the solutions are derived.

Stability analysis for a partial element equivalent circuit (PEEC) model of neutral type

This paper is concerned with the problem of robust stability analysis for a partial element equivalent circuit (PEEC) model of neutral type. Based on Lyapunov stability theory and a linear matrix inequality (LMI) approach, some sufficient delay-dependent stability conditions are derived. A numerical example shows that the result using the method in the paper is less conservative than that using some existing methods in the literature. Copyright © 2005 John Wiley & Sons, Ltd.

Robust stability of some oscillatory systems including time-varying delay with applications in congestion control

Abstract This paper focuses on the stability of some second-order linear systems with multiple constant and time-varying delays, under the assumption that the corresponding system without delays is an oscillator. Sufficient conditions for delay-dependent stability will be derived using the integral quadratic constraint approach combined with the generalized eigenvalue distribution of some appropriate finite-dimensional matrix pencils. As applications, we shall discuss some fluid approximation models used in congestion control of high-speed networks, under the natural assumptions that the control-time intervals are constant, but the round-trip times are time-varying.

On delay-dependent stability for linear neutral systems

This paper focuses on the problem of uniform asymptotic stability of a class of linear neutral systems. Sufficient conditions for delay-dependent stability are given in terms of the existence of solutions of some linear matrix inequalities. Furthermore, the proposed technique extends to neutral systems the results obtained for delay-difference equations using model transformations. Illustrative examples are included.

On delay-dependent stability under model transformations of some neutral linear systems

This paper focuses on the stability analysis of a class of neutral linear systems. Some sufficient delay-dependent stability conditions are derived in terms of an appropriate model transformation of the original system, transformation similar to the one used in the retarded case. The analysis makes use of an appropriate construction of a degenerate Lyapunov-Krasovskii functional. Several computational schemes and frequency-domain interpretations, as well as an example are also presented.

On delay dependent stability for linear neutral systems

This paper focuses on the problem of uniform asymptotic stability of a class of linear neutral systems. The delays are assumed to be unknown, but constant. Sufficient conditions for delay-dependent stability are given in terms of the existence of symmetric and positive definite solutions of some linear matrix inequalities. Furthermore, the proposed technique extends the results obtained for delay-difference equations to neutral systems using model transformations. The derived results are illustrated by a numerical example.