scholarly journals Robust H∞ Consensus Control for Linear Discrete-Time Swarm Systems with Parameter Uncertainties and Time-Varying Delays

2019 ◽  
Vol 2019 ◽  
pp. 1-16
Author(s):  
Xiao Jia ◽  
Laihong Hu ◽  
Fujun Feng ◽  
Jun Xu
Keyword(s):  
Control Problem ◽  
Discrete Time ◽  
Convergence Result ◽  
Linear Matrix ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Consensus Protocol ◽  
Consensus Control ◽  
Consensus Analysis ◽  
The Stability

Robust H∞ consensus control problems of linear swarm systems with parameter uncertainties and time-varying delays are investigated. In this literature, a linear consensus protocol for high-order discrete-time swarm systems is proposed. Firstly, the robust H∞ consensus control problem of discrete-time swarm systems is transformed into a robust H∞ control problem of a set of independent uncertain systems. Secondly, sufficient linear matrix inequality conditions for robust H∞ consensus analysis of discrete-time swarm systems are given by the stability theory, and a H∞ performance level γ is determined meanwhile. Thirdly, the convergence result is derived as a final consensus value of swarm systems. Finally, numerical examples are presented to demonstrate theoretical results.

Fuzzy Control for Nonlinear Uncertain T-S Fuzzy Systems with Time-Varying Delays

2013 ◽  
Vol 341-342 ◽  
pp. 668-673
Author(s):  
Yi Min Li ◽  
Yuan Yuan Li
Keyword(s):  
Stability Analysis ◽  
Discrete Time ◽  
Fuzzy Model ◽  
Optimization Techniques ◽  
Linear Matrix ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Lmi Optimization ◽  
System A ◽  
The Stability

This paper studies the stability analysis of discrete time-varying system with parameter uncertainties and disturbances. The system under consideration is subject to time-varying non-bounded parameter uncertainties in both the state and measured output matrices. To facilitate the stability analysis, the T-S fuzzy model is employed to represent the discrete-time nonlinear system. A fuzzy observer is used to guarantee the Lyapunov stability of the closed-loop system and reduces the effect of the disturbance input on the controlled output to a prescribed level for all admissible uncertainties. The control and observer matrices can be obtained by directly solving a set of linear matrix inequality (LMI) via the existing LMI optimization techniques. Finally, an example is provided to demonstrate the effectiveness of the proposed approach.

scholarly journals Robust Synchronization Criterion for Coupled Stochastic Discrete-Time Neural Networks with Interval Time-Varying Delays, Leakage Delay, and Parameter Uncertainties

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
M. J. Park ◽  
O. M. Kwon ◽  
Ju H. Park ◽  
S. M. Lee ◽  
E. J. Cha
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Leakage Term ◽  
Interval Time ◽  
Robust Synchronization ◽  
Delay Dependent ◽  
Finsler’S Lemma

The purpose of this paper is to investigate a delay-dependent robust synchronization analysis for coupled stochastic discrete-time neural networks with interval time-varying delays in networks coupling, a time delay in leakage term, and parameter uncertainties. Based on the Lyapunov method, a new delay-dependent criterion for the synchronization of the networks is derived in terms of linear matrix inequalities (LMIs) by constructing a suitable Lyapunov-Krasovskii’s functional and utilizing Finsler’s lemma without free-weighting matrices. Two numerical examples are given to illustrate the effectiveness of the proposed methods.

Robust stabilization and H∞ control for discrete-time stochastic genetic regulatory networks with time delays

2012 ◽  
Vol 90 (10) ◽  
pp. 939-953 ◽  
Author(s):  
K. Mathiyalagan ◽  
R. Sakthivel
Keyword(s):  
Discrete Time ◽  
Regulatory Networks ◽  
Robust Stabilization ◽  
Genetic Regulatory Networks ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Time Varying Delay ◽  
Stochastic Genetic Regulatory Networks

This paper presents some novel results on robust stabilization and H∞ control design for a class of uncertain discrete-time stochastic genetic regulatory networks (GRNs) with time-varying delays. The GRNs under consideration are subject to stochastic noise, time-varying, and norm bounded parameter uncertainties. By constructing a new Lyapunov–Krasovskii functional that contains some novel triple summation terms, we propose a state feedback gene controller to guarantee that the considered GRN is mean-square asymptotically stable about its equilibrium point for all admissible uncertainties. The other issue is to design a H∞ feedback gene controller so that the GRN is robustly stable with a prescribed H∞ disturbance attenuation level for all admissible uncertainties and for all delays to satisfy both the lower bound and upper bound of the interval time-varying delay. The obtained conditions are derived in terms of linear matrix inequalities (LMIs), which can be easily verified via the LMI toolbox. Finally, the control scheme has been implemented in a gene network model to illustrate the applicability and usefulness of the obtained results.

Stability analysis for discrete-time neural networks with time-varying delays and stochastic parameter uncertainties

2015 ◽  
Vol 93 (4) ◽  
pp. 398-408 ◽  
Author(s):  
O.M. Kwon ◽  
M.J. Park ◽  
S.M. Lee ◽  
E.J. Cha
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Parameter Uncertainties ◽  
Stochastic Parameter ◽  
Delay Dependent ◽  
Delay Dependent Stability

This paper proposes new delay-dependent stability criteria for discrete-time neural networks with interval time-varying delays and probabilistic occurring parameter uncertainties. It is assumed that parameter uncertainties are changed with the environment, explored using random situations, and its stochastic information is included in the proposed method. By constructing a suitable Lyapunov–Krasovskii functional, new delay-dependent stability criteria for the concerned systems are established in terms of linear matrix inequalities, which can be easily solved by various effective optimization algorithms. Two numerical examples are given to illustrate the effectiveness of the proposed method.

scholarly journals Improved Criteria on Delay-Dependent Stability for Discrete-Time Neural Networks with Interval Time-Varying Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
O. M. Kwon ◽  
M. J. Park ◽  
Ju H. Park ◽  
S. M. Lee ◽  
E. J. Cha
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Lyapunov Method ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Interval Time ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability

The purpose of this paper is to investigate the delay-dependent stability analysis for discrete-time neural networks with interval time-varying delays. Based on Lyapunov method, improved delay-dependent criteria for the stability of the networks are derived in terms of linear matrix inequalities (LMIs) by constructing a suitable Lyapunov-Krasovskii functional and utilizing reciprocally convex approach. Also, a new activation condition which has not been considered in the literature is proposed and utilized for derivation of stability criteria. Two numerical examples are given to illustrate the effectiveness of the proposed method.

Fuzzy Control of a Class of Discrete-Time Fuzzy Bilinear Systems with Time-Delay

2012 ◽  
Vol 482-484 ◽  
pp. 1881-1885
Author(s):  
Jian Hu Jiang ◽  
Chao Wu ◽  
Yun Wang Ge ◽  
Li Jun Song
Keyword(s):  
Discrete Time ◽  
Sufficient Conditions ◽  
Bilinear System ◽  
Stability Control ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
The Stability ◽  
Varying Delay

The stability control problem is considered for a class of discrete-time T-S fuzzy bilinear system with time-varying delay in both state and input. Based on the parallel distribute compensation (PDC) scheme, some sufficient conditions are derived to guarantee the global asymptotically stability of the overall fuzzy system, which are represented in terms of matrix inequality. The corresponding controller can be obtained by solving a set of linear matrix inequalities. Finally, a simulation example shows that the approach is effective.

H ∞ Guaranteed Cost Filtering for Uncertain Discrete-Time Switched Systems With Multiple Time-Varying Delays

2010 ◽  
Vol 133 (1) ◽  
Author(s):  
Haibin Sun ◽  
Guangdeng Zong ◽  
Linlin Hou
Keyword(s):  
Discrete Time ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Multiple Time ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Guaranteed Cost ◽  
The Cost

This paper deals with the problem of H∞ guaranteed cost filtering for uncertain discrete-time switched systems with multiple time-varying delays. The switched system under consideration is subject to time-varying norm-bounded parameter uncertainties in all the system matrices. The aim is to design a filter, which guarantees the asymptotical stability of the error system with prescribed disturbance attenuation for all admissible uncertainties and the cost function value is not more than a specified upper bound. By resorting to a switched Lyapunov function, some delay-dependent sufficient conditions are presented in terms of linear matrix inequalities. A numerical example is provided to demonstrate the effectiveness of the proposed algorithms.

scholarly journals Further Results Concerning Delay-DependentH∞Control for Uncertain Discrete-Time Systems with Time-Varying Delay

2009 ◽  
Vol 2009 ◽  
pp. 1-24 ◽  
Author(s):  
Guangdeng Zong ◽  
Linlin Hou ◽  
Hongyong Yang
Keyword(s):  
Discrete Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Closed Loop System ◽  
Parameter Uncertainties ◽  
Time Varying Delay ◽  
Discrete Time Systems ◽  
Delay Dependent ◽  
Time Systems ◽  
Varying Delay

This paper addresses the problem ofH∞control for uncertain discrete-time systems with time-varying delays. The system under consideration is subject to time-varying norm-bounded parameter uncertainties in both the state and controlled output. Attention is focused on the design of a memoryless state feedback controller, which guarantees that the resulting closed-loop system is asymptotically stable and reduces the effect of the disturbance input on the controlled output to a prescribed level irrespective of all the admissible uncertainties. By introducing some slack matrix variables, new delay-dependent conditions are presented in terms of linear matrix inequalities (LMIs). Numerical examples are provided to show the reduced conservatism and lower computational burden than the previous results.

Observer-Based H∞ Feedback Control for Arbitrarily Time-Varying Discrete-Time Systems With Intermittent Measurements and Input Constraints

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Hui Zhang ◽  
Yang Shi
Keyword(s):  
Feedback Control ◽  
Control Problem ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Discrete Time Systems ◽  
Intermittent Measurements ◽  
Time Systems ◽  
Intermittent Measurement

In this paper, we investigate the observer-based H∞ feedback control problem for discrete-time systems subject intermittent measurements and constrained control inputs. To characterize the practical scenario of the intermittent measurement phenomenon, we model it using a stochastic Bernoulli approach. We assume that the control action is constrained to be below a prescribed level. Sufficient conditions are obtained for the observer-based H∞ feedback control problem. The estimator and the controller are derived by solving a linear matrix inequality (LMI)-based optimization problem. Moreover, the proposed method is extended to systems with arbitrarily time-varying parameters within a polytope with unknown vertices. Three examples are given to illustrate the effectiveness and efficacy of the proposed method.

scholarly journals Delay-Range-Dependent Global Robust Passivity Analysis of Discrete-Time Uncertain Recurrent Neural Networks with Interval Time-Varying Delay

2009 ◽  
Vol 2009 ◽  
pp. 1-14 ◽  
Author(s):  
Chien-Yu Lu ◽  
Chin-Wen Liao ◽  
Hsun-Heng Tsai
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Recurrent Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Interval Time ◽  
Time Varying Delay ◽  
Passivity Analysis ◽  
Varying Delay

This paper examines a passivity analysis for a class of discrete-time recurrent neural networks (DRNNs) with norm-bounded time-varying parameter uncertainties and interval time-varying delay. The activation functions are assumed to be globally Lipschitz continuous. Based on an appropriate type of Lyapunov functional, sufficient passivity conditions for the DRNNs are derived in terms of a family of linear matrix inequalities (LMIs). Two numerical examples are given to illustrate the effectiveness and applicability.

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