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 Global Dissipativity on Uncertain Discrete-Time Neural Networks with Time-Varying Delays

2010 ◽  
Vol 2010 ◽  
pp. 1-19 ◽  
Author(s):  
Qiankun Song ◽  
Jinde Cao
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Discrete Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Computationally Efficient ◽  
Inequality Technique ◽  
General Activation ◽  
Delay Dependent

The problems on global dissipativity and global exponential dissipativity are investigated for uncertain discrete-time neural networks with time-varying delays and general activation functions. By constructing appropriate Lyapunov-Krasovskii functionals and employing linear matrix inequality technique, several new delay-dependent criteria for checking the global dissipativity and global exponential dissipativity of the addressed neural networks are established in linear matrix inequality (LMI), which can be checked numerically using the effective LMI toolbox in MATLAB. Illustrated examples are given to show the effectiveness of the proposed criteria. It is noteworthy that because neither model transformation nor free-weighting matrices are employed to deal with cross terms in the derivation of the dissipativity criteria, the obtained results are less conservative and more computationally efficient.

Observer-Based Stabilization of Linear Discrete Time-Varying Delay Systems

2021 ◽  
Author(s):  
Venkatesh Modala ◽  
Sourav Patra ◽  
Goshaidas Ray
Keyword(s):  
Discrete Time ◽  
Upper Bound ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Stabilizing Controller ◽  
Time Varying Delay ◽  
Convex Inequality ◽  
Summation Inequality ◽  
Delay Dependent

Abstract This paper presents the design of an observer-based stabilizing controller for linear discrete-time systems subject to interval time-varying state-delay. In this work, the problem has been formulated in convex optimization framework by constructing a new Lyapunov-Krasovskii (LK) functional to derive a delay-dependent stabilization criteria. The summation inequality and the extended reciprocally convex inequality are exploited to obtain a less conservative delay upper bound in linear matrix inequality (LMI) framework. The derived stability conditions are delay-dependent and thus, ensure global asymptotic stability in presence of any time delay less than the obtained delay upper bound. Numerical examples are included to demonstrate the usefulness of the developed results.

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 New Delay-Dependent Robust Stability Criterion for LPD Discrete-Time Systems with Interval Time-Varying Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Narongsak Yotha ◽  
Kanit Mukdasai
Keyword(s):  
Robust Stability ◽  
Discrete Time ◽  
Model Transformation ◽  
Linear Matrix ◽  
Time Varying ◽  
Interval Time ◽  
Discrete Time Systems ◽  
Delay Dependent ◽  
Parameter Dependent ◽  
Time Systems

This paper investigates the problem of robust stability for linear parameter-dependent (LPD) discrete-time systems with interval time-varying delays. Based on the combination of model transformation, utilization of zero equation, and parameter-dependent Lyapunov-Krasovskii functional, new delay-dependent robust stability conditions are obtained and formulated in terms of linear matrix inequalities (LMIs). Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.

Delay-Dependent Robust Control for Discrete-Time Uncertain Stochastic Systems With Time-Varying Delays

2017 ◽  
Vol 139 (10) ◽  
Author(s):  
Cheung-Chieh Ku ◽  
Guan-Wei Chen
Keyword(s):  
Robust Control ◽  
Discrete Time ◽  
Stochastic Systems ◽  
Design Method ◽  
Sufficient Conditions ◽  
Jensen Inequality ◽  
Linear Matrix ◽  
Time Varying ◽  
Gain Scheduled Controller ◽  
Delay Dependent

This paper investigates a delay-dependent robust control problem of discrete-time uncertain stochastic systems with delays. The uncertainty considered in this paper is time-varying but norm-bounded, and the delays are considered as interval time-varying case for both state and input. According to the considerations of uncertainty, stochastic behavior, and time delays, the problem considered in this paper is more general than the existing works for uncertain stochastic systems. Via the proposed Lyapunov–Krasovskii function, some sufficient conditions are derived into the extended linear matrix inequality form. Moreover, Jensen inequality and free matrix equation are employed to reduce conservatism of those conditions. Through using the proposed design method, a gain-scheduled controller is designed to guarantee asymptotical stability of uncertain stochastic systems in the sense of mean square. Finally, two numerical examples are provided to demonstrate applicability and effectiveness of the proposed design method.

scholarly journals StochasticH∞Control for Discrete-Time Singular Systems with State and Disturbance Dependent Noise

2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
Yong Zhao ◽  
Xiushan Jiang ◽  
Weihai Zhang
Keyword(s):  
Discrete Time ◽  
State Feedback ◽  
Closed Loop ◽  
Singular Systems ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Mean Square ◽  
Matrix Inequalities ◽  
Closed Loop System ◽  
Theoretical Results

This paper is concerned with the stochasticH∞state feedback control problem for a class of discrete-time singular systems with state and disturbance dependent noise. Two stochastic bounded real lemmas (SBRLs) are proposed via strict linear matrix inequalities (LMIs). Based on the obtained SBRLs, a state feedbackH∞controller is presented, which not only guarantees the resulting closed-loop system to be mean square admissible but also satisfies a prescribedH∞performance level. A numerical example is finally given to illustrate the effectiveness of the proposed theoretical results.

scholarly journals Robust Exponential Stability for LPD Discrete-Time System with Interval Time-Varying Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Kanit Mukdasai
Keyword(s):  
Exponential Stability ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Discrete Time System ◽  
Time System ◽  
Robust Exponential Stability ◽  
Time Varying Delay ◽  
Varying Delay

This paper investigates the problem of robust exponential stability for uncertain linear-parameter dependent (LPD) discrete-time system with delay. The delay is of an interval type, which means that both lower and upper bounds for the time-varying delay are available. The uncertainty under consideration is norm-bounded uncertainty. Based on combination of the linear matrix inequality (LMI) technique and the use of suitable Lyapunov-Krasovskii functional, new sufficient conditions for the robust exponential stability are obtained in terms of LMI. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.

CLUSTER SYNCHRONIZATION OF DISCRETE-TIME STOCHASTIC COMPLEX DYNAMICAL NETWORKS WITH PROBABILISTIC INTERVAL TIME-VARYING DELAYS

2012 ◽  
Vol 26 (05) ◽  
pp. 1250037 ◽  
Author(s):  
HONGJIE LI
Keyword(s):  
Discrete Time ◽  
Cluster Synchronization ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Nonlinear Functions ◽  
Interval Time ◽  
Analysis Techniques ◽  
Binary Switch ◽  
Delay Dependent

The paper investigates the cluster synchronization in discrete-time complex networks with stochastic nonlinearities and probabilistic interval time-varying delays. Based on the stochastic analysis techniques and the properties of the Kronecker product, delay-dependent cluster synchronization stability criteria are derived in the form of linear matrix inequalities. The solvability of derived conditions depends on not only the probability of the binary switch between nonlinear functions, but also the size of the delay and the probability of the delay taking values in some intervals. Finally, a numerical simulation is provided to illustrate the effectiveness of the proposed criterion.

scholarly journals Robust aperiodic-disturbance rejection in an uncertain modified repetitive-control system

2016 ◽  
Vol 26 (2) ◽  
pp. 285-295 ◽  
Author(s):  
Lan Zhou ◽  
Jinhua She ◽  
Chaoyi Li ◽  
Changzhong Pan
Keyword(s):  
Control System ◽  
Output Feedback ◽  
Disturbance Rejection ◽  
Closed Loop ◽  
Repetitive Control ◽  
Linear Matrix ◽  
Time Varying ◽  
Dimensional Model ◽  
Closed Loop System ◽  
Output Feedback Controller

Abstract This paper concerns the problem of designing an EID-based robust output-feedback modified repetitive-control system (ROFMRCS) that provides satisfactory aperiodic-disturbance rejection performance for a class of plants with time-varying structured uncertainties. An equivalent-input-disturbance (EID) estimator is added to the ROFMRCS that estimates the influences of all types of disturbances and compensates them. A continuous-discrete two-dimensional model is built to describe the EID-based ROFMRCS that accurately presents the features of repetitive control, thereby enabling the control and learning actions to be preferentially adjusted. A robust stability condition for the closed-loop system is given in terms of a linear matrix inequality. It yields the parameters of the repetitive controller, the output-feedback controller, and the EID-estimator. Finally, a numerical example demonstrates the validity of the method.

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