scholarly journals New Approach on Robust and Reliable Decentralized H∞ Tracking Control for Fuzzy Interconnected Systems with Time-Varying Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Xinrui Liu ◽  
Qiuye Sun ◽  
Xinming Hou
Keyword(s):  
Tracking Control ◽  
Large Scale ◽  
Direct Method ◽  
Descriptor Systems ◽  
Interconnected Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Actuator Failures ◽  
Varying Delay

This paper investigates the robust and reliable decentralized H∞ tracking control issue for the fuzzy large-scale interconnected systems with time-varying delay, which are composed of a number of T-S fuzzy subsystems with interconnections. Firstly, the ordinary fuzzy interconnected systems are equivalently transformed to the fuzzy descriptor systems; then, according to the Lyapunov direct method and the decentralized control theory of large-scale interconnected systems, the new linear matrix inequalities- (LMIs-) based conditions with some free variables are derived to guarantee the H∞ tracking performance not only when all control components are operating well, but also in the presence of some possible actuator failures. Moreover, there is no need for the precise failure parameters of the actuators, rather than the lower and upper bound. Finally, two simulation examples are provided to illustrate the effectiveness of the proposed method.

State feedback stabilization of linear descriptor time-varying delay systems

2020 ◽  
Vol 42 (12) ◽  
pp. 2191-2197 ◽  
Author(s):  
Piyapong Niamsup ◽  
Vu N Phat
Keyword(s):  
State Feedback ◽  
Sufficient Conditions ◽  
Feedback Stabilization ◽  
Descriptor Systems ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Delay Function ◽  
Time Varying Delay ◽  
Varying Delay

In this paper, the augmented Lyapunov-Krasovskii function approach combining with singular value decomposition method is developed for stabilization of linear descriptor systems with time-varying delay. The delay function is non-differentiable, but continuous and bounded. By introducing a set of improved Lyapunov-Krasovskii functionals we propose delay-dependent sufficient conditions for admissibility of the system in terms of linear matrix inequalities. Then, based on the obtained stability results the problem of stabilization is solved via state feedback controllers, which guarantees that the descriptor closed-loop system is admissible. An numerical example with simulation is provided to show the effectiveness of the theoretical result.

A new control approach for a class of linear switched systems with time-varying delay

2021 ◽  
pp. 014233122199272
Author(s):  
Abbas Zabihi Zonouz ◽  
Mohammad Ali Badamchizadeh ◽  
Amir Rikhtehgar Ghiasi
Keyword(s):  
Stability Analysis ◽  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Switching Systems ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Linear Switching Systems ◽  
The Stability ◽  
Varying Delay

In this paper, a new method for designing controller for linear switching systems with varying delay is presented concerning the Hurwitz-Convex combination. For stability analysis the Lyapunov-Krasovskii function is used. The stability analysis results are given based on the linear matrix inequalities (LMIs), and it is possible to obtain upper delay bound that guarantees the stability of system by solving the linear matrix inequalities. Compared with the other methods, the proposed controller can be used to get a less conservative criterion and ensures the stability of linear switching systems with time-varying delay in which delay has way larger upper bound in comparison with the delay bounds that are considered in other methods. Numerical examples are given to demonstrate the effectiveness of proposed method.

scholarly journals Improved Stability Criteria of Static Recurrent Neural Networks with a Time-Varying Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Lei Ding ◽  
Hong-Bing Zeng ◽  
Wei Wang ◽  
Fei Yu
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Improved Stability ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper investigates the stability of static recurrent neural networks (SRNNs) with a time-varying delay. Based on the complete delay-decomposing approach and quadratic separation framework, a novel Lyapunov-Krasovskii functional is constructed. By employing a reciprocally convex technique to consider the relationship between the time-varying delay and its varying interval, some improved delay-dependent stability conditions are presented in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to show the merits and the effectiveness of the proposed methods.

scholarly journals Convex Polyhedron Method to Stability of Continuous Systems with Two Additive Time-Varying Delay Components

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Tiejun Li ◽  
Junkang Tian
Keyword(s):  
Stability Criterion ◽  
Convex Polyhedron ◽  
Linear Matrix ◽  
Continuous Systems ◽  
Time Varying ◽  
Time Varying Delay ◽  
Polyhedron Method ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper is concerned with delay-dependent stability for continuous systems with two additive time-varying delay components. By constructing a new class of Lyapunov functional and using a new convex polyhedron method, a new delay-dependent stability criterion is derived in terms of linear matrix inequalities. The obtained stability criterion is less conservative than some existing ones. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.

scholarly journals Robust Stability of a Class of Uncertain Lur'e Systems of Neutral Type

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
W. Weera ◽  
P. Niamsup
Keyword(s):  
Neutral Type ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Lur’E Systems ◽  
Interval Time ◽  
Delay Function ◽  
Time Varying Delay ◽  
Bounded Nonlinearity ◽  
Varying Delay

This paper deals with the problem of stability for a class of Lur’e systems with interval time-varying delay and sector-bounded nonlinearity. The interval time-varying delay function is not assumed to be differentiable. We analyze the global exponential stability for uncertain neutral and Lur’e dynamical systems with some sector conditions. By constructing a set of improved Lyapunov-Krasovskii functional combined with Leibniz-Newton’s formula, we establish some stability criteria in terms of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness of the results.

Exponential Stability for Stochastic Neural Networks with Time-Varying Delay and Leakage Delay

2015 ◽  
Vol 742 ◽  
pp. 399-403
Author(s):  
Ya Jun Li ◽  
Jing Zhao Li
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Leakage Delay ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Varying Delay

This paper investigates the exponential stability problem for a class of stochastic neural networks with leakage delay. By employing a suitable Lyapunov functional and stochastic stability theory technic, the sufficient conditions which make the stochastic neural networks system exponential mean square stable are proposed and proved. All results are expressed in terms of linear matrix inequalities (LMIs). Example and simulation are presented to show the effectiveness of the proposed method.

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