Delay Dependent Stability Analysis of Active Power Filter

2012 ◽  
Vol 220-223 ◽  
pp. 1592-1597
Author(s):  
Tao Li ◽  
Yong Qiang Liu
Keyword(s):  
Time Delay ◽  
Active Power Filter ◽  
Negative Influence ◽  
Active Power ◽  
Delay Systems ◽  
Linear Matrix ◽  
Power Filter ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability

The active power filter (APF) is a dynamic harmonic filtering equipment. The time delay is unavoidable and it has a great negative influence on the stability of the APF system. Based on the introduction of its topology and control strategy, the mathematical model of APF with time delay is built. And the model is a time delay systems with bounded nonlinearity, so a new delay dependent stability criteria is derived and formulated in the form of linear matrix inequality (LMI). The maximum allowed time delay is solved, and the relationships between it and some other parameters are investigated and simulated. The result can be as a reference in the future work.

Stability of nonlinear time-delay systems satisfying a quadratic constraint

2016 ◽  
Vol 40 (3) ◽  
pp. 712-718 ◽  
Author(s):  
Mohsen Ekramian ◽  
Mohammad Ataei ◽  
Soroush Talebi
Keyword(s):  
Time Delay ◽  
Uncertain Systems ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Matrix Inequalities ◽  
Quadratic Constraint ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability

The stability problem of nonlinear time-delay systems is addressed. A quadratic constraint is employed to exploit the structure of nonlinearity in dynamical systems via a set of multiplier matrices. This yields less conservative results concerning stability analysis. By employing a Wirtinger-based inequality, a delay-dependent stability criterion is derived in terms of linear matrix inequalities for the nominal and uncertain systems. A numerical example is used to demonstrate the effectiveness of the proposed stability conditions in dealing with some larger class of nonlinearities.

scholarly journals Improved Delay-Dependent Stability and Stabilization Conditions of T-S Fuzzy Time-Delay Systems via an Augmented Lyapunov-Krasovskii Functional Approach

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Zifan Gao ◽  
Jiaxiu Yang ◽  
Shuqian Zhu
Keyword(s):  
Time Delay ◽  
Delay Systems ◽  
Linear Matrix ◽  
Stability Conditions ◽  
State Variables ◽  
Time Varying Delay ◽  
Improved Stability ◽  
Stability And Stabilization ◽  
The Stability ◽  
Delay Dependent

This paper develops some improved stability and stabilization conditions of T-S fuzzy system with constant time-delay and interval time-varying delay with its derivative bounds available, respectively. These conditions are presented by linear matrix inequalities (LMIs) and derived by applying an augmented Lyapunov-Krasovskii functional (LKF) approach combined with a canonical Bessel-Legendre (B-L) inequality. Different from the existing LKFs, the proposed LKF involves more state variables in an augmented way resorting to the form of the B-L inequality. The B-L inequality is also applied in ensuring the positiveness of the constructed LKF and the negativeness of derivative of the LKF. By numerical examples, it is verified that the obtained stability conditions can ensure a larger upper bound of time-delay, the larger number of Legendre polynomials in the stability conditions can lead to less conservative results, and the stabilization condition is effective, respectively.

scholarly journals ANALYZE THE EFFECT OF TIME DELAY ON THE STABILITY OF HYBRID ACTIVE POWER FILTER

2022 ◽  
Vol 36 (06) ◽  
Author(s):  
CHAU MINH THUYEN
Keyword(s):  
Time Delay ◽  
Active Power Filter ◽  
Active Power ◽  
Practical Significance ◽  
Stable Domain ◽  
Power Filter ◽  
Hybrid Active Power Filter ◽  
The Stability ◽  
And Control ◽  
The Mathematical Model

Hybrid Active Power Filter (HAPF) has highly effective in improving the power quality of power system. In this paper, a stable analysis of HAPF considering the time delay was made. The mathematical model of HAPF with time delay has been established. Based on that, the stable domain of the HAPF parameters was determined based on the Routh’s stability standard. Simulation results based on Matlab software have shown that: time delay has a marked impact on the stability of the HAPF system. This research has practical significance in the design and control of HAPF in real system.

scholarly journals Delay-Dependent Stability of Uncertain Distributed Time-Delay Systems

2012 ◽  
Vol 6-7 ◽  
pp. 45-48
Author(s):  
Cheng Wang ◽  
Qing Zhang ◽  
Jian Ping Gan
Keyword(s):  
Time Delay ◽  
Delay Systems ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequality ◽  
Time Delay Systems ◽  
Parameter Uncertainties ◽  
Distributed Time Delay ◽  
Delay Dependent ◽  
Delay Dependent Stability

In this paper, the problem of stability analysis of uncertain distributed time-delay systems is investigated. Systems with norm-bounded parameter uncertainties are considered. By taking suitable Lyapunov-Krasovskii functional and free weighting matrices, a delay-dependent sufficient condition is derived in terms of linear matrix inequality (LMI). The condition obtained in this paper can be tested numerically very efficiently using interior point algorithms.

New Approach to Delay-Dependent Control for Fuzzy Time-Delay Systems

2012 ◽  
Vol 482-484 ◽  
pp. 291-299
Author(s):  
Gang Guo
Keyword(s):  
Time Delay ◽  
Fuzzy Systems ◽  
Control Method ◽  
Delay Systems ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
New Approach ◽  
Stabilization Condition ◽  
Delay Dependent ◽  
Delay Dependent Stability

A new control method is proposed for stability analysis and stabilization problems for T-S fuzzy systems with time-delay. A new fuzzy Lyapunov-Krasovskii functional is introduced to establish some delay-dependent stability criteria. Based on parallel distributed compensation (PDC) scheme, a delay-dependent stabilization condition is derived and the corresponding controller can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, simulation examples show that the effectiveness and benefits of the proposed method.

scholarly journals The Influence of Shunt Active Power Filter on Stability and Performance in Considering Time-Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Tao Li ◽  
Yongqiang Liu
Keyword(s):  
Time Delay ◽  
Performance Index ◽  
Great Influence ◽  
Active Power Filter ◽  
Stability Margin ◽  
Delay System ◽  
Active Power ◽  
Linear Matrix ◽  
Power Filter ◽  
And Performance

The existence of time-delay in active power filter (APF) has a great influence on its stability and performance. Hence, this paper deals with the problems of solving the delay margin, the maximal delay which allows the closed-loop system to retain stable, and minimizing the performance index for a givenH∞controller. Firstly, for the given time-delay system and controller, a Lyapunov-Krasovskii functional is used to derive a delay-dependent stability criterion. And a modified Lyapunov-Krasovskii functional is used to obtain less conservative results. Secondly, the mathematical model of APF with time-delay is built, and the two problems already mentioned can be dealt with via transforming them into one of the basic problems of linear matrix inequality (LMI). Finally, the relationships between the delay stability margin and some parameters have been investigated, and the performance index has been discussed in considering time-delay. The effectiveness of the proposed method is verified by simulation studies.

scholarly journals A New Integral Inequality and Delay-Decomposition with Uncertain Parameter Approach to the Stability Analysis of Time-Delay Systems

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Haiyang Zhang ◽  
Lianglin Xiong ◽  
Qing Miao ◽  
Yanmeng Wang ◽  
Chen Peng
Keyword(s):  
Time Delay ◽  
Integral Inequality ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Decomposition Approach ◽  
Delay Decomposition Approach ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Delay Decomposition

This paper is concerned with the problem of delay-dependent stability of time-delay systems. Firstly, it introduces a new useful integral inequality which has been proved to be less conservative than the previous inequalities. Next, the inequality combines delay-decomposition approach with uncertain parameters applied to time-delay systems, based on the new Lyapunov-Krasovskii functionals and new stability criteria for system with time-delay have been derived and expressed in terms of LMIs. Finally, a numerical example is provided to show the effectiveness and the less conservative feature of the proposed method compared with some recent results.

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