Robust State Feedback H∞ Control for Discrete-Time Fuzzy System With Random Delays

2017 ◽  
Vol 139 (8) ◽  
Author(s):  
R. Sakthivel ◽  
A. Arunkumar ◽  
K. Mathiyalagan ◽  
Ju H. Park
Keyword(s):  
Time Delay ◽  
Discrete Time ◽  
State Feedback ◽  
Robust Stabilization ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Control Input ◽  
Time Varying Delay ◽  
Random Delays ◽  
Distribution Probability

This paper investigates the problem of robust stabilization for a class of discrete-time Takagi–Sugeno (TS) fuzzy systems via input random delays in control input. The main objective of this paper is to design a state feedback H∞ controller. Linear matrix inequality (LMI) approach together with the construction of proper Lyapunov–Krasovskii functional is employed for obtaining delay dependent sufficient conditions for the existence of robust H∞ controller. In particular, the effect of both variation range and distribution probability of the time delay is taken into account in the control input. The key feature of the proposed results in this paper is that the time‐varying delay in the control input not only dependent on the bound but also the distribution probability of the time delay. The obtained results are formulated in terms of LMIs which can be easily solved by using the standard optimization algorithms. Finally, a numerical example with simulation result is provided to illustrate the effectiveness of the obtained control law and less conservativeness of the proposed result.

scholarly journals Synchronization of Discrete-Time Stochastic Neural Networks with Random Delay

2011 ◽  
Vol 2011 ◽  
pp. 1-20 ◽  
Author(s):  
Haibo Bao ◽  
Jinde Cao
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Stochastic Neural Networks ◽  
Time Varying Delay ◽  
Random Delays ◽  
Random Fashion ◽  
Analysis Technique

By using a Lyapunov-Krasovskii functional method and the stochastic analysis technique, we investigate the problem of synchronization for discrete-time stochastic neural networks (DSNNs) with random delays. A control law is designed, and sufficient conditions are established that guarantee the synchronization of two identical DSNNs with random delays. Compared with the previous works, the time delay is assumed to be existent in a random fashion. The stochastic disturbances are described in terms of a Brownian motion and the time-varying delay is characterized by introducing a Bernoulli stochastic variable. Two examples are given to illustrate the effectiveness of the proposed results. The main contribution of this paper is that the obtained results are dependent on not only the bound but also the distribution probability of the time delay. Moreover, our results provide a larger allowance variation range of the delay, and are less conservative than the traditional delay-independent ones.

Modeling and Fuzzy Control for Complex Flexible Nonlinear Systems with Time-Delay

2014 ◽  
Vol 602-605 ◽  
pp. 920-923
Author(s):  
Ji Xiang Chen
Keyword(s):  
Time Delay ◽  
Feedback Control ◽  
Nonlinear Systems ◽  
Discrete Time ◽  
State Feedback ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Control Approach ◽  
Fuzzy State

A time-delay discrete-time fuzzy singularly perturbed modeling and fuzzy state feedback control approach are presented for a class of complex flexible nonlinear systems with time-delay. The considered flexible nonlinear system is firstly described by a time-delay standard discrete-time fuzzy singular perturbation model. A fuzzy state feedback control law is secondly design. By using a matrix spectral norm and linear matrix inequalities approach, the sufficient conditions of the controller existence are divided. The provided controller not only can stabilize the resulting closed-loop system but also overcome the effects caused by both time-delay and external disturbances. A simulation example is given to illustrate the effectiveness of the developed result.

Fuzzy observer–based disturbance rejection control for nonlinear fractional-order systems with time-varying delay

2021 ◽  
pp. 107754632110069
Author(s):  
Parvin Mahmoudabadi ◽  
Mahsan Tavakoli-Kakhki
Keyword(s):  
Fractional Order ◽  
Disturbance Rejection ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Delayed Systems ◽  
Fuzzy Observer ◽  
Time Varying Delay ◽  
Takagi Sugeno

In this article, a Takagi–Sugeno fuzzy model is applied to deal with the problem of observer-based control design for nonlinear time-delayed systems with fractional-order [Formula: see text]. By applying the Lyapunov–Krasovskii method, a fuzzy observer–based controller is established to stabilize the time-delayed fractional-order Takagi–Sugeno fuzzy model. Also, the problem of disturbance rejection for the addressed systems is studied via the state-feedback method in the form of a parallel distributed compensation approach. Furthermore, sufficient conditions for the existence of state-feedback gains and observer gains are achieved in the terms of linear matrix inequalities. Finally, two numerical examples are simulated for the validation of the presented methods.

Exponential synchronization of a Markovian jump complex dynamic network with piecewise-constant transition rates and distributed delay

2018 ◽  
Vol 41 (9) ◽  
pp. 2535-2544 ◽  
Author(s):  
Nasim Akbari ◽  
Ali Sadr ◽  
Ali Kazemy
Keyword(s):  
Time Delay ◽  
Sufficient Conditions ◽  
Distributed Delay ◽  
Dynamic Network ◽  
Exponential Synchronization ◽  
Linear Matrix ◽  
Transition Rates ◽  
Markovian Jump ◽  
Piecewise Constant ◽  
Time Varying Delay

The exponential synchronization of a Markovian jump complex dynamical network with piecewise-constant transition rates is investigated. Two distinct types of time-varying delay are considered for the system; one is distributed time-delay for each node, the other is discrete coupling time-delay. Based on an augmented Lyapunov–Krasovskii functional, some sufficient conditions are derived and expressed in the form of linear matrix inequalities, which are formulated in such a manner as to determine the controller gain matrices. Finally, an example is given to illustrate the effectiveness and validity of the proposed method.

Further Results on Exponential Stability and State Feedback Stabilization for Time Delay Singular Saturating Actuator Systems With Delay-Dependence

2017 ◽  
Vol 139 (10) ◽  
Author(s):  
Pin-Lin Liu
Keyword(s):  
Time Delay ◽  
Convex Optimization ◽  
State Feedback ◽  
Singular Systems ◽  
Sufficient Conditions ◽  
Feedback Stabilization ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Decision Variables ◽  
Delay Dependence

This paper will study the exponential stable and state feedback stabilization of time delay singular systems with saturation actuators. Some sufficient conditions for existence of controller are obtained by using the linear matrix inequalities (LMIs) and integral inequality approach (IIA). When these LMIs are feasible, an explicit expression of controller is obtained. Based on Lyapunov–Krasovskii functional (LKF) techniques, a novel exponential stabilization criterion has been also derived in terms of LMIs which can be easily solved with efficient convex optimization algorithm. Our results are less conservative than some existing ones, and the decision variables involved in this paper are less than them. Examples illustrate our results as less conservative than those reported in the literature.

scholarly journals Robust Stabilization of Discrete-Time Systems with Time-Varying Delay: An LMI Approach

2008 ◽  
Vol 2008 ◽  
pp. 1-15 ◽  
Author(s):  
Valter J. S. Leite ◽  
Márcio F. Miranda
Keyword(s):  
Robust Stability ◽  
Discrete Time ◽  
Robust Stabilization ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Discrete Time Systems ◽  
Robust Stability Analysis ◽  
Time Systems ◽  
Varying Delay

Sufficient linear matrix inequality (LMI) conditions to verify the robust stability and to design robust state feedback gains for the class of linear discrete-time systems with time-varying delay and polytopic uncertainties are presented. The conditions are obtained through parameter-dependent Lyapunov-Krasovskii functionals and use some extra variables, which yield less conservative LMI conditions. Both problems, robust stability analysis and robust synthesis, are formulated as convex problems where all system matrices can be affected by uncertainty. Some numerical examples are presented to illustrate the advantages of the proposed LMI conditions.

scholarly journals RobustH∞Control for Linear Stochastic Partial Differential Systems with Time Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Xisheng Dai ◽  
Feiqi Deng ◽  
Jianxiang Zhang
Keyword(s):  
Time Delay ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Linear Matrix ◽  
Mean Square ◽  
Feedback Controllers ◽  
Partial Differential ◽  
Mean Square Exponential Stability ◽  
Linear Matrix Inequality Approach

This paper investigates the problems of robust stochastic mean square exponential stabilization and robustH∞for stochastic partial differential time delay systems. Sufficient conditions for the existence of state feedback controllers are proposed, which ensure mean square exponential stability of the resulting closed-loop system and reduce the effect of the disturbance input on the controlled output to a prescribed level ofH∞performance. A linear matrix inequality approach is employed to design the desired state feedback controllers. An illustrative example is provided to show the usefulness of the proposed technique.

scholarly journals Robust Exponential Stabilization of Uncertain Impulsive Bilinear Time-Delay Systems with Saturating Actuators

2010 ◽  
Vol 2010 ◽  
pp. 1-6 ◽  
Author(s):  
Yang Shujie ◽  
Shi Bao ◽  
Zhang Qiang ◽  
Pan Tetie
Keyword(s):  
Time Delay ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Exponential Stabilization ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Time Dynamics ◽  
Saturating Actuators ◽  
Robust Exponential Stabilization

This paper investigates the problem of robust exponential stabilization for uncertain impulsive bilinear time-delay systems with saturating actuators. By using the Lyapunov function and Razumikhin-type techniques, two classes of impulsive systems are considered: the systems with unstable discrete-time dynamics and the ones with stable discrete-time dynamics. Sufficient conditions for robust stabilization are obtained in terms of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness of the theoretical results.

NOVEL STABILITY CRITERIA ON DISCRETE-TIME NEURAL NETWORKS WITH BOTH TIME-VARYING AND DISTRIBUTED DELAYS

2009 ◽  
Vol 19 (04) ◽  
pp. 269-283 ◽  
Author(s):  
TAO LI ◽  
AIGUO SONG ◽  
SHUMIN FEI
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Convex Combination ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Robust Exponential Stability ◽  
Time Varying Delay ◽  
Weighting Matrix ◽  
Combination Methods

This paper investigates robust exponential stability for discrete-time recurrent neural networks with both time-varying delay (0 ≤ τm ≤ τ(k) ≤ τM) and distributed one. Through partitioning delay intervals [0,τm] and [τm,τM], respectively, and choosing an augmented Lyapunov-Krasovskii functional, the delay-dependent sufficient conditions are obtained by using free-weighting matrix and convex combination methods. These criteria are presented in terms of linear matrix inequalities (LMIs) and their feasibility can be easily checked by resorting to LMI in Matlab Toolbox in Ref. 1. The activation functions are not required to be differentiable or strictly monotonic, which generalizes those earlier forms. As an extension, we further consider the robust stability of discrete-time delayed Cohen-Grossberg neural networks. Finally, the effectiveness of the proposed results is further illustrated by three numerical examples in comparison with the reported ones.

scholarly journals Finite-Time Nonfragile Dissipative Control for Discrete-Time Neural Networks with Markovian Jumps and Mixed Time-Delays

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Ling Hou ◽  
Dongyan Chen ◽  
Chan He
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Existence Condition ◽  
Mode Switching ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Time Varying Delay ◽  
Mixed Time Delays

This paper considers the stochastic finite-time dissipative (SFTD) control problem based on nonfragile controller for discrete-time neural networks (NNS) with Markovian jumps and mixed delays, in which the mode switching phenomenon, is described as Markov chain, and the mixed delays are composed of discrete time-varying delay and distributed delays. First, by selecting an appropriate Lyapunov-Krasovskii functional and applying stochastic analysis methods, some parameters-dependent sufficient conditions for solvability of stochastic finite-time boundedness are derived. Then, the main results are extended to SFTD control. Furthermore, existence condition of nonfragile controller is derived based on solution of linear matrix inequalities (LMIs). Finally, two numerical examples are employed to show the effectiveness of the obtained methods.

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