scholarly journals A Delay-Dependent Approach to Stability of Uncertain Discrete-Time State-Delayed Systems with Generalized Overflow Nonlinearities

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
V. Krishna Rao Kandanvli ◽  
Haranath Kar
Keyword(s):  
Asymptotic Stability ◽  
Discrete Time ◽  
Global Asymptotic Stability ◽  
Parameter Uncertainties ◽  
Delayed Systems ◽  
Numerical Example ◽  
Delay Dependent

This paper addresses the problem of global asymptotic stability of a class of uncertain discrete-time state-delayed systems employing generalized overflow nonlinearities. The systems under investigation involve parameter uncertainties that are assumed to be deterministic and norm bounded. A new computationally tractable delay-dependent criterion for global asymptotic stability of such systems is presented. A numerical example is given to illustrate the effectiveness of the proposed method.

scholarly journals An LMI Based Criterion for Global Asymptotic Stability of Discrete-Time State-Delayed Systems with Saturation Nonlinearities

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Priyanka Kokil
Keyword(s):  
Asymptotic Stability ◽  
Discrete Time ◽  
Global Asymptotic Stability ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Delayed Systems ◽  
State Delays ◽  
Discrete Time Systems ◽  
Multiple State ◽  
Time Systems

A linear matrix inequality (LMI) based criterion for the global asymptotic stability of discrete-time systems with multiple state-delays employing saturation nonlinearities is presented. Numerical examples highlighting the effectiveness of the proposed criterion are given.

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.

scholarly journals Delay-Partitioning Approach to Stability of Linear Discrete-Time Systems with Interval-Like Time-Varying Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Priyanka Kokil ◽  
V. Krishna Rao Kandanvli ◽  
Haranath Kar
Keyword(s):  
Asymptotic Stability ◽  
Discrete Time ◽  
Global Asymptotic Stability ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Discrete Time Systems ◽  
Time Systems ◽  
Delay Partitioning ◽  
Varying Delay

This paper is concerned with the problem of global asymptotic stability of linear discrete-time systems with interval-like time-varying delay in the state. By utilizing the concept of delay partitioning, a new linear-matrix-inequality-(LMI-) based criterion for the global asymptotic stability of such systems is proposed. The proposed criterion does not involve any free weighting matrices but depends on both the size of delay and partition size. The developed approach is extended to address the problem of global asymptotic stability of state-delayed discrete-time systems with norm-bounded uncertainties. The proposed results are compared with several existing results.

scholarly journals New Stability Criterion for Takagi-Sugeno Fuzzy Cohen-Grossberg Neural Networks with Probabilistic Time-Varying Delays

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Xiongrui Wang ◽  
Ruofeng Rao ◽  
Shouming Zhong
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Stability Criterion ◽  
Global Asymptotic Stability ◽  
Positive Definite ◽  
Time Varying ◽  
Numerical Example ◽  
Definite Form ◽  
Takagi Sugeno

A new global asymptotic stability criterion of Takagi-Sugeno fuzzy Cohen-Grossberg neural networks with probabilistic time-varying delays was derived, in which the diffusion item can play its role. Owing to deleting the boundedness conditions on amplification functions, the main result is a novelty to some extent. Besides, there is another novelty in methods, for Lyapunov-Krasovskii functional is the positive definite form of p powers, which is different from those of existing literature. Moreover, a numerical example illustrates the effectiveness of the proposed methods.

scholarly journals Robust Moving HorizonH∞Control of Discrete Time-Delayed Systems with Interval Time-Varying Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
F. Yıldız Tascikaraoglu ◽  
I. B. Kucukdemiral ◽  
J. Imura
Keyword(s):  
Discrete Time ◽  
Disturbance Rejection ◽  
Closed Loop ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Time Varying ◽  
Discrete Time System ◽  
Delayed Systems ◽  
State Delays ◽  
Delay Dependent

In this study, design of a delay-dependent type moving horizon state-feedback control (MHHC) is considered for a class of linear discrete-time system subject to time-varying state delays, norm-bounded uncertainties, and disturbances with bounded energies. The closed-loop robust stability and robust performance problems are considered to overcome the instability and poor disturbance rejection performance due to the existence of parametric uncertainties and time-delay appeared in the system dynamics. Utilizing a discrete-time Lyapunov-Krasovskii functional, some delay-dependent linear matrix inequality (LMI) based conditions are provided. It is shown that if one can find a feasible solution set for these LMI conditions iteratively at each step of run-time, then we can construct a control law which guarantees the closed-loop asymptotic stability, maximum disturbance rejection performance, and closed-loop dissipativity in view of the actuator limitations. Two numerical examples with simulations on a nominal and uncertain discrete-time, time-delayed systems, are presented at the end, in order to demonstrate the efficiency of the proposed method.

scholarly journals Stabilization of Discrete-Time Delayed Systems via Partially Delay-Dependent Controllers

2015 ◽  
Vol 2015 ◽  
pp. 1-14
Author(s):  
Guoliang Wang ◽  
Boyu Li
Keyword(s):  
Discrete Time ◽  
State Feedback ◽  
Transition Probabilities ◽  
Stabilization Problem ◽  
Delayed Systems ◽  
Stabilizing Controller ◽  
Discrete Time Markov Chain ◽  
Distribution Property ◽  
Special Cases ◽  
Delay Dependent

This paper is concerned with the stabilization problem for a class of discrete-time delayed systems, whose stabilizing controller is firstly designed to be partially delay-dependent. The distribution property of such a controller is firstly described by a discrete-time Markov chain with two modes. It is seen that two traditionally special cases of state feedback controller without or with time delay, respectively, are included. Based on the proposed controller, new stabilization conditions depending on some probabilities are developed. Because of the established results with LMI forms, they are further extended to more general cases that the transition probabilities are uncertain and totally unknown, while more applications are also given in detail. Finally, numerical examples are used to demonstrate the effectiveness and superiority of the proposed methods.

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