Delay-Dependent γ-Suboptimal H∞ Model Reduction for Neutral Systems With Time-Varying Delays

2005 ◽  
Vol 128 (2) ◽  
pp. 394-399 ◽  
Author(s):  
Qing Wang ◽  
James Lam ◽  
Shengyuan Xu ◽  
Liqian Zhang
Keyword(s):  
Model Reduction ◽  
Linear Matrix ◽  
Optimization Approach ◽  
Time Varying ◽  
Neutral Systems ◽  
Order Model ◽  
Reduced Order ◽  
Reduction Problem ◽  
Bounded Realness ◽  
Delay Dependent

In this paper, the model reduction problem of neutral systems with time-varying delays is studied with γ suboptimality under the H∞ measure. A delay-dependent bounded realness condition of the H∞ norm is given via linear matrix inequalities (LMIs). Based on such a condition, a sufficient condition to characterize the existence of the reduced-order models is given in terms of LMIs with inverse constraints. By employing a sequential convex optimization approach, a reduced-order model can be computed with H∞ error less than some prescribed scalar γ.

scholarly journals H∞ Model Reduction of 2D Markovian Jump System with Roesser Model

2012 ◽  
Vol 6-7 ◽  
pp. 135-142
Author(s):  
Xue Song Han ◽  
Yu Bo Duan
Keyword(s):  
Model Reduction ◽  
Reduced Order Model ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Roesser Model ◽  
Markovian Jump ◽  
Order Model ◽  
Existence Of A Solution ◽  
Reduced Order ◽  
Jump Systems

This paper extends the results obtained for one-dimensional Markovian jump systems to investigate the problem of H∞model reduction for a class of linear discrete time 2D Markovian jump systems with state delays in Roesser model which is time-varying and mode-independent. The reduced-order model with the same randomly jumping parameters is proposed which can make the error systems stochastically stable with a prescribed H∞ performance. A sufficient condition in terms of linear matrix inequalitiesSubscript text(LMIs) plus matrix inverse constraints are derived for the existence of a solution to the reduced-order model problems. The cone complimentarity linearization (CCL) method is exploited to cast them into nonlinear minimization problems subject to LMI constraints. A numerical example is given to illustrate the design procedures.

scholarly journals New Delay-Dependent Exponential Stability Criteria for Neural Networks with Mixed Time-Varying Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-16
Author(s):  
Wu Wen ◽  
Kaibo Shi
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Linear Matrix ◽  
Optimization Approach ◽  
Time Varying ◽  
Stability Criteria ◽  
Decision Variables ◽  
Mathematical Techniques ◽  
Delay Dependent ◽  
The Relationship

This study is concerned with the problem of new delay-dependent exponential stability criteria for neural networks (NNs) with mixed time-varying delays via introducing a novel integral inequality approach. Specifically, first, by taking fully the relationship between the terms in the Leibniz-Newton formula into account, several improved delay-dependent exponential stability criteria are obtained in terms of linear matrix inequalities (LMIs). Second, together with some effective mathematical techniques and a convex optimization approach, less conservative conditions are derived by constructing an appropriate Lyapunov-Krasovskii functional (LKF). Third, the proposed methods include the least numbers of decision variables while keeping the validity of the obtained results. Finally, three numerical examples with simulations are presented to illustrate the validity and advantages of the theoretical results.

scholarly journals Robust Stability Criteria for Uncertain Neutral Systems with Interval Nondifferentiable Time-Varying Delay and Nonlinear Perturbations

2011 ◽  
Vol 2011 ◽  
pp. 1-20 ◽  
Author(s):  
W. Weera ◽  
P. Niamsup
Keyword(s):  
Robust Stability ◽  
Linear Matrix ◽  
Fast Time ◽  
Time Varying ◽  
Nonlinear Perturbations ◽  
Stability Criteria ◽  
Neutral Systems ◽  
Time Varying Delay ◽  
Delay Dependent ◽  
Varying Delay

We study the robust stability criteria for uncertain neutral systems with interval time-varying delays and time-varying nonlinear perturbations simultaneously. The constraint on the derivative of the time-varying delay is not required, which allows the time-delay to be a fast time-varying function. Based on the Lyapunov-Krasovskii theory, we derive new delay-dependent stability conditions in terms of linear matrix inequalities (LMIs) which can be solved by various available algorithms. Numerical examples are given to demonstrate that the derived conditions are much less conservative than those given in the literature.

On Stability of Neutral Systems with Time-Varying Delay

2011 ◽  
Vol 50-51 ◽  
pp. 22-26
Author(s):  
Mei Lan Tang ◽  
Xin Ge Liu
Keyword(s):  
Linear Matrix ◽  
Time Varying ◽  
Discrete Delay ◽  
Neutral Systems ◽  
Neutral Delay ◽  
Time Varying Delay ◽  
Discrete Delays ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper investigates the delay-dependent robust stability of neutral systems with time-varying discrete delays and time-varying structured uncertainties. New delay-dependent stability criteria are obtained and formulated in the form of a linear matrix inequality. Since the criteria take the sizes of the neutral delay, discrete delay and derivative of discrete delay into account, they are less conservative than previous methods. Numerical example is given to indicate significant improvements over some existing results.

Exponential Stability for Uncertain Switched Neutral Systems with Nonlinear Perturbations

2011 ◽  
Vol 217-218 ◽  
pp. 668-673
Author(s):  
Xiu Liu ◽  
Shou Ming Zhong ◽  
Xiu Yong Ding
Keyword(s):  
Exponential Stability ◽  
Linear Matrix ◽  
Time Varying ◽  
Nonlinear Perturbations ◽  
Neutral Systems ◽  
Weighting Matrix ◽  
The Stability ◽  
Switched Neutral Systems ◽  
Delay Dependent ◽  
Stability Results

The global exponential stability for switched neutral systems with time-varying delays and nonlinear perturbations is investigated in this paper. LMI-based delay-dependent criterion is proposed to guarantee exponential stability for our considered systems under any switched signal. Lyapunov-Krasovskii functional and Leibniz-Newton formula are applied to find the stability results. Free weighting matrix and linear matrix inequality (LMI) approaches are used to solve the proposed conditions.

scholarly journals Improved Results on Delay-Dependent Robust H ∞ Control of Uncertain Neutral Systems with Mixed Time-Varying Delays

2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Jingsha Zhang ◽  
Yongke Li ◽  
Xiaolin Ma ◽  
Zhilong Lin ◽  
Changlong Wang
Keyword(s):  
State Feedback ◽  
Controller Design ◽  
The State ◽  
Linear Matrix ◽  
Feedback Gain ◽  
Time Varying ◽  
Neutral Systems ◽  
The Matrix ◽  
Left And Right ◽  
Delay Dependent

In this paper, the problem of the delay-dependent robust H ∞ control for a class of uncertain neutral systems with mixed time-varying delays is studied. Firstly, a robust delay-dependent asymptotic stability criterion is shown by linear matrix inequalities (LMIs) after introducing a new Lyapunov–Krasovskii functional (LKF). The LKF including vital terms is expected to obtain results of less conservatism by employing the technique of various efficient convex optimization algorithms and free matrices. Then, based on the obtained criterion, analyses for uncertain systems and H ∞ controller design are presented. Moreover, on the analysis of the state-feedback controller, different from the traditional method which multiplies the matrix inequality left and right by some matrix and its transpose, respectively, we can obtain the state-feedback gain directly by calculating the LMIs through the toolbox of MATLAB in this paper. Finally, the feasibility and validity of the method are illustrated by examples.

scholarly journals New Delay-Dependent Stability Criteria for Uncertain Neutral Systems with Mixed Time-Varying Delays and Nonlinear Perturbations

2009 ◽  
Vol 2009 ◽  
pp. 1-22 ◽  
Author(s):  
Hamid Reza Karimi ◽  
Mauricio Zapateiro ◽  
Ningsu Luo
Keyword(s):  
Sufficient Conditions ◽  
Distributed Delay ◽  
Linear Matrix ◽  
Time Varying ◽  
Neutral Systems ◽  
Neutral Delay ◽  
Change Of Variables ◽  
Parameter Perturbations ◽  
The Stability ◽  
Delay Dependent

The problem of stability analysis for a class of neutral systems with mixed time-varying neutral, discrete and distributed delays and nonlinear parameter perturbations is addressed. By introducing a novel Lyapunov-Krasovskii functional and combining the descriptor model transformation, the Leibniz-Newton formula, some free-weighting matrices, and a suitable change of variables, new sufficient conditions are established for the stability of the considered system, which are neutral-delay-dependent, discrete-delay-range-dependent, and distributed-delay-dependent. The conditions are presented in terms of linear matrix inequalities (LMIs) and can be efficiently solved using convex programming techniques. Two numerical examples are given to illustrate the efficiency of the proposed method.

Hysteresis Switching Design for Stabilization of Switched Neutral Systems Using Multiple Lyapunov Functionals

2012 ◽  
Author(s):  
Tai-Fang Li ◽  
Georgi M. Dimirovski ◽  
Jun Zhao
Keyword(s):  
Discrete Time ◽  
Linear Matrix ◽  
Lyapunov Functionals ◽  
Time Varying ◽  
Neutral Systems ◽  
Switching Law ◽  
Time Varying Delay ◽  
Switched Neutral Systems ◽  
Delay Dependent ◽  
Varying Delay

The stabilization problem for a class of switched neutral systems with a discrete time-varying delay is studied in this paper. The upper bound of derivative of the discrete time-varying delay can be an arbitrary given constant which is not necessary to be less than one. Each subsystem is not assumed to be stable. A hysteresis switching law is designed based on multiple Lyapunov functionals to avoid sliding modes and chattering phenomena. The obtained delay-dependent stabilization criterion is given in terms of linear matrix inequalities (LMIs). The result is illustrated by an example.

scholarly journals New Delay-Dependent Robust Exponential Stability Criteria of LPD Neutral Systems with Mixed Time-Varying Delays and Nonlinear Perturbations

2013 ◽  
Vol 2013 ◽  
pp. 1-18 ◽  
Author(s):  
Sirada Pinjai ◽  
Kanit Mukdasai
Keyword(s):  
Exponential Stability ◽  
Coefficient Matrix ◽  
Linear Matrix ◽  
Time Varying ◽  
Nonlinear Perturbations ◽  
Stability Criteria ◽  
Neutral Systems ◽  
Robust Exponential Stability ◽  
Delay Dependent ◽  
Parameter Dependent

This paper is concerned with the problem of robust exponential stability for linear parameter-dependent (LPD) neutral systems with mixed time-varying delays and nonlinear perturbations. Based on a new parameter-dependent Lyapunov-Krasovskii functional, Leibniz-Newton formula, decomposition technique of coefficient matrix, free-weighting matrices, Cauchy’s inequality, modified version of Jensen’s inequality, model transformation, and linear matrix inequality technique, new delay-dependent robust exponential stability criteria are established in terms of linear matrix inequalities (LMIs). Numerical examples are given to show the effectiveness and less conservativeness of the proposed methods.

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