Delay-dependent Linear Matrix Inequality Research Articles

Robust asymptotic stability for BAM neural networks with time-varying delays via LMI approach

Several novel stability conditions for BAM neural networks with time-varying delays are studied. Based on Lyapunov-Krasovskii functional combined with linear matrix inequality approach, the delay-dependent linear matrix inequality (LMI) conditions are established to guarantee robust asymptotic stability for given delayed BAM neural networks. These criteria can be easily verified by utilizing the recently developed algorithms for solving LMIs. A numerical example is provided to demonstrate the effectiveness and less conservatism of the main results.

Stability and robust stabilisation for uncertain discrete stochastic hybrid singular systems with time delay

The stochastic stability and robust stochastic stabilisation for time-delay discrete Markovian jump singular systems with parameter uncertainties are discussed. Based on stochastic Lyapunov functional, a delay-dependent linear matrix inequalities (LMIs) condition for the time-delay discrete Markovian jump singular systems to be regular, causal and stochastically stable is given. With this condition, the problem of robust stochastic stabilisation is solved. A numerical example to illustrate the effectiveness of the method is given.

Stability of uncertain piecewise affine systems with time delay: delay-dependent Lyapunov approach

This article addresses the problem of robust stability of piecewise affine (PWA) uncertain systems with unknown time-varying delay in the state. It is assumed that the uncertainty is norm bounded and that upper bounds on the state delay and its rate of change are available. A set of linear matrix inequalities (LMIs) is derived providing sufficient conditions for the stability of the system. These conditions depend on the upper bound of the delay. The main contributions of the article are as follows. First, new delay-dependent LMI conditions are derived for the stability of PWA time-delay systems. Second, the stability conditions are extended to the case of uncertain PWA time delay systems. Numerical examples are presented to show the effectiveness of the approach.

New exponentially convergent state estimation method for delayed neural networks

The problem of designing a globally exponentially convergent state estimator for a class of delayed neural networks is investigated in this paper. The time-delay pattern is quite general and including fast time-varying delays. The activation functions are monotone nondecreasing with known lower and upper bounds. A linear estimator of Luenberger-type is developed and by properly constructing a new Lyapunov–Krasovskii functional coupled with the integral inequality, the global exponential stability conditions of the error system are derived. The unknown gain matrix is determined by solving a delay-dependent linear matrix inequality. The developed results are shown to be less conservative than previously published ones in the literature, which is illustrated by a representative numerical example.

Robust filtering for stochastic genetic regulatory networks with time-varying delay

This paper addresses the robust filtering problem for a class of linear genetic regulatory networks (GRNs) with stochastic disturbances, parameter uncertainties and time delays. The parameter uncertainties are assumed to reside in a polytopic region, the stochastic disturbance is state-dependent described by a scalar Brownian motion, and the time-varying delays enter into both the translation process and the feedback regulation process. We aim to estimate the true concentrations of mRNA and protein by designing a linear filter such that, for all admissible time delays, stochastic disturbances as well as polytopic uncertainties, the augmented state estimation dynamics is exponentially mean square stable with an expected decay rate. A delay-dependent linear matrix inequality (LMI) approach is first developed to derive sufficient conditions that guarantee the exponential stability of the augmented dynamics, and then the filter gains are parameterized in terms of the solution to a set of LMIs. Note that LMIs can be easily solved by using standard software packages. A simulation example is exploited in order to illustrate the effectiveness of the proposed design procedures.

Robust H∞ filtering for uncertain discrete Markov jump singular systems with mode-dependent time delay

The robust H∞ filtering problem for mode-dependent time-delay discrete Markov jump singular systems with parameter uncertainties is discussed. Based on delay-dependent linear matrix inequalities, a Markov jump filter is designed, which guarantees that the filtering error system is regular, causal, stochastically stable and satisfies H∞ performance for all admissible uncertainties. The H∞ filter can be of full or of a reduced order. A numerical example is given to illustrate the effectiveness of the proposed method.

상태와 입력에 시변 시간지연을 가지는 불확실 이산시간 특이시스템의 지연종속 강인 안정화 및 비약성 제어

This paper deals with the design problem of robust stabilization and non-fragile controller for discrete-time singular systems with parameter uncertainties and time-varying delays in state and input by delay-dependent Linear Matrix Inequality (LMI) approach. A new delay-dependent bounded real lemma for singular systems with time-varying delays is derived. Robust stabilization and robust non-fragile state feedback control laws are proposed, which guarantees that the resultant closed-loop system is regular, causal and stable in spite of time-varying delays, parameter uncertainties, and controller gain variations. A numerical example is given to show the validity of the design method.

Robust H-Infinity Filter Design for Uncertain Linear Systems Over Network with Network-Induced Delays and Output Quantization

This paper investigates a convex optimization approach to the problem of robustH1 ltering for uncertain linear systems connected over a common digital communication network. We consider the case where quantizers are static and the parameter uncertainties are norm bounded. Firstly, we propose a new model to investigate the eect of both the output quantization levels and the network conditions. Secondly, by introducing a descriptor technique, using Lyapunov-Krasovskii functional and a suitable change of variables, new required sucient conditions are established in terms of delay-dependent linear matrix inequalities (LMIs) for the existence of the desired network-based quantized lters with simultaneous consideration of network induced delays and measurement quantization. The explicit expression of the lters is derived to satisfy both asymptotic stability and a prescribed level of disturbance attenuation for all admissible norm bounded uncertainties.

Further results on state estimation for neural networks of neutral-type with time-varying delay

In this paper, further result on design problem of state estimator for a class of neural networks of neutral type is presented. A delay-dependent linear matrix inequality (LMI) criterion for existence of the estimator is derived. A numerical simulation is given to show the effectiveness of proposed estimator.

Delay-dependent stability and [formula omitted] control for uncertain discrete switched singular systems with time-delay

The robust stability, robust stabilization and H ∞ control problems for time-delay discrete switched singular systems with parameter uncertainties are discussed. Based on the restricted system equivalent (r.s.e.) transformation and by introducing new state vectors, the switched singular system is transformed into a switched standard linear system, and delay-dependent linear matrix inequality (LMI) conditions for the time-delay discrete-time switched singular systems to be regular, causal and uniformly asymptotically stable; uniformly robust asymptotically stable with γ-disturbance attenuation are obtained, respectively. With these conditions, robust stabilization problem and robust H ∞ control problem are solved based on LMIs.

State estimation for neural networks of neutral-type with interval time-varying delays

In this paper, the design problem of state estimator for a class of neural networks of neutral-type with interval time-varying delays is studied. The interval time-varying delay does not have constraint that its derivative is less than 1. The constraint is widely used to deal with time-varying delays in many papers. A delay-dependent linear matrix inequality (LMI) criterion for existence of the estimator is proposed by using Lyapunov method. The criterion can be easily solved by various convex optimization algorithms. A numerical example is given to show the effectiveness of proposed method.

Design of state estimator for neural networks of neutral-type

In this paper, the design problem of state estimator for a class of neural networks of neutral-type is studied. A delay-dependent linear matrix inequality (LMI) criterion for existence of the estimator is proposed by using the Lyapunov method. The criterion can be easily solved by various convex optimization algorithms. A numerical example with simulation results is given to show the effectiveness of proposed method.

LMI-based criterion for global asymptotic stability of BAM neural networks with time delays

This paper presents a stability criterion for global asymptotic stability of the equilibrium point for Bidirectional Associative Memory (BAM) neural networks with fixed time delays. An approach combining the Lyapunov-Krasovskii functional with Linear Matrix Inequality (LMI) is taken to investigate the stability of the system. A delay-dependent LMI criterion is derived. Finally, a numerical example is given to illustrate the results.

Observer-Based $H_{\infty}$ Control for T–S Fuzzy Systems With Time Delay: Delay-Dependent Design Method

This correspondence studies the problem of observer-based H infinity control for time-delay Takagi-Sugeno (T-S) fuzzy systems. It provides a delay-dependent linear matrix inequality (LMI)-based method for the control design. It is known that the key important problem in the literature, even for delay-independent case, lies in the difficulty of decoupling matrix variables in corresponding matrix inequalities. This correspondence suggests a decoupling technique for solving matrix inequalities with coupled variables, and provides an LMI-based algorithm by adopting the idea of the cone complementarity problem. The derivation relies on the appropriate choice of Lyaponuv-Krasovskii functionals which incorporate the intersections among local systems. Illustrative examples are given to show the effectiveness of the present delay-dependent result.

Delay-dependent robust stability and stabilisation for uncertain discrete singular systems with time-varying delays

The robust stability and robust stabilisation problems for time-varying delay discrete singular systems with parameter uncertainties are discussed. A delay-dependent linear matrix inequality (LMI) condition to enable time-varying delay discrete standard state-space systems to be stable is given. Based on this condition and the restricted system equivalent transformation, the delay-dependent LMI condition is proposed for the time-varying delay discrete singular systems to be admissible. With this condition, the problems of robust stability and robust stabilisation are solved, and the delay-dependent LMI conditions are obtained. Numerical examples illustrate the effectiveness of the proposed method.

Delay-dependent stability and stabilization of uncertain discrete-time markovian jump singular systems with time delay

This paper discusses robust stochastic stability and stabilization of time-delay discrete Markovian jump singular systems with parameter uncertainties. Based on the restricted system equivalent (RES) transformation, a delay-dependent linear matrix inequalities condition for time-delay discrete-time Markovian jump singular systems to be regular, causal and stochastically stable is established. With this condition, problems of robust stochastic stability and stabilization are solved, and delay-dependent linear matrix inequalities are obtained. A numerical example is also given to illustrate the effectiveness of this method.2000Mathematics subject classification: primary 39A12; secondary 93C55.

Delay-dependent stabilization of stochastic interval delay systems with nonlinear disturbances

In this paper, a delay-dependent approach is developed to deal with the robust stabilization problem for a class of stochastic time-delay interval systems with nonlinear disturbances. The system matrices are assumed to be uncertain within given intervals, the time delays appear in both the system states and the nonlinear disturbances, and the stochastic perturbation is in the form of a Brownian motion. The purpose of the addressed stochastic stabilization problem is to design a memoryless state feedback controller such that, for all admissible interval uncertainties and nonlinear disturbances, the closed-loop system is asymptotically stable in the mean square, where the stability criteria are dependent on the length of the time delay and therefore less conservative. By using Itô's differential formula and the Lyapunov stability theory, sufficient conditions are first derived for ensuring the stability of the stochastic interval delay systems. Then, the controller gain is characterized in terms of the solution to a delay-dependent linear matrix inequality (LMI), which can be easily solved by using available software packages. A numerical example is exploited to demonstrate the effectiveness of the proposed design procedure.

A delay-dependent LMI approach to dynamics analysis of discrete-time recurrent neural networks with time-varying delays

In this Letter, the analysis problem for the existence and stability of periodic solutions is investigated for a class of general discrete-time recurrent neural networks with time-varying delays. For the neural networks under study, a generalized activation function is considered, and the traditional assumptions on the boundedness, monotony and differentiability of the activation functions are removed. By employing the latest free-weighting matrix method, an appropriate Lyapunov–Krasovskii functional is constructed and several sufficient conditions are established to ensure the existence, uniqueness, and globally exponential stability of the periodic solution for the addressed neural network. The conditions are dependent on both the lower bound and upper bound of the time-varying time delays. Furthermore, the conditions are expressed in terms of the linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. Two simulation examples are given to show the effectiveness and less conservatism of the proposed criteria.

A Less Conservative Robust Stability Test for Linear Uncertain Time-Delay Systems

This note concerns with the robust stability of linear uncertain systems with state-delay. The uncertainty is assumed to be of polytopic type. A less conservative delay-dependent linear matrix inequality (LMI) method is presented based on a new Lyapunov-Krasovskii functional. The present method incorporates a relaxed parameter-dependent technique combined with a recently proposed idea of introducing free-weighting matrices. When confined to delay-free case, the present result is also less conservative than existing stability tests using parameter-dependent methods. Numerical examples are given to show the less conservativeness of the results.

H∞ disturbance attenuation for uncertain mechanical systems with input delay

The paper deals with the robust H disturbance attenuation problem for uncertain mechanical systems with input delay. The parameter uncertainties for the mass, damping and stiffness matrices take an additive a priori norm-bounded form. The time delay for the input is time-invariant but has a known constant bound. A robust static H state-feedback controller is designed to attenuate the disturbance on the controlled output to a prescribed level for all admissible parameter uncertainties and input delay. The design approach is formulated in terms of the feasibility of certain delay-dependent linear matrix inequalities. A numerical example is employed to illustrate the effectiveness of the approach.