scholarly journals Disturbance Rejection for Fractional-Order Time-Delay Systems

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Hai-Peng Jiang ◽  
Yong-Qiang Liu
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Disturbance Rejection ◽  
Controller Design ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Design Algorithm ◽  
The Stability ◽  
Disturbance Estimator

This paper presents an equivalent-input-disturbance (EID-) based disturbance rejection method for fractional-order time-delay systems. First, a modified state observer is applied to reconstruct the state of the fractional-order time-delay plant. Then, a disturbance estimator is designed to actively compensate for the disturbances. Under such a construction of the system, by constructing a novel monochromatic Lyapunov function and using direct Lyapunov approach, the stability analysis and controller design algorithm are derived in terms of linear matrix inequality (LMI) technique. Finally, simulation results demonstrate the validity of the proposed method.

A new approach for periodic disturbance rejection in input-time-delay systems

2017 ◽  
Vol 40 (8) ◽  
pp. 2589-2598 ◽  
Author(s):  
Xin Chen ◽  
Wenjing Cai ◽  
Min Wu ◽  
Weihua Cao
Keyword(s):  
Time Delay ◽  
Stability Criterion ◽  
Disturbance Rejection ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Design Algorithm ◽  
Periodic Disturbance ◽  
Small Gain ◽  
Input Time ◽  
The Stability

An innovative approach combining equivalent-input-disturbance (EID) theory with the internal model principle is applied to achieve periodic disturbance rejection in input-time-delay systems. The EID estimator, which exhibits the synthetic effect of the time-delay and the periodic disturbance as an input-dependent disturbance, is constructed by inserting appropriate time-delay elements to compensate for the total influence of the input-time-delay and the periodic disturbance. A sufficient stability criterion is derived based on the separation theorem and the small-gain theorem. A design algorithm is developed for the system based on the stability criterion. Design and simulation results for the example are also employed to compare our method with the disturbance observer approach, and to demonstrate the validity of our method.

scholarly journals Anti-Saturation Control of Uncertain Time-Delay Systems with Actuator Saturation Constraints

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 375
Author(s):  
Hejun Yao
Keyword(s):  
Time Delay ◽  
Controller Design ◽  
Actuator Saturation ◽  
Design Method ◽  
Lyapunov Stability Theory ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Saturation Control ◽  
Systems Model

The problem of anti-saturation control for a class of time-delay systems with actuator saturation is considered in this paper. By introducing appropriate variable substitution, a new delay time-delay systems model with actuator saturation systems is established. Based on the Lyapunov stability theory, the stability condition and the anti-saturation controller design method are obtained by using the linear matrix inequality approach. By introducing the matrix into the Lyapunov function, the proposed conditions are less conservative than the previous results. Finally, a simulation example shows the validity and rationality of the method.

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 An algebraic stability test for fractional order time delay systems

2020 ◽  
Vol 10 (1) ◽  
pp. 94-103 ◽  
Author(s):  
Münevver Mine Özyetkin ◽  
Dumitru Baleanu
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Test Procedure ◽  
Stability Test ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Delay Term ◽  
Square Roots ◽  
Algebraic Stability ◽  
The Stability

In this study, an algebraic stability test procedure is presented for fractional order time delay systems. This method is based on the principle of eliminating time delay. The stability test of fractional order systems cannot be examined directly using classical methods such as Routh-Hurwitz, because such systems do not have analytical solutions. When a system contains the square roots of s, it is seen that there is a double value function of s. In this study, a stability test procedure is applied to systems including sqrt(s) and/or different fractional degrees such as s^alpha where 0 < ? < 1, and ? include in R. For this purpose, the integer order equivalents of fractional order terms are first used and then the stability test is applied to the system by eliminating time delay. Thanks to the proposed method, it is not necessary to use approximations instead of time delay term such as Pade. Thus, the stability test procedure does not require the solution of higher order equations. 

State Feedback Stabilization in Nonlinear Time-Delay Systems

2002 ◽  
Vol 6 (3) ◽  
pp. 109-114
Author(s):  
Tsuyoshi Hori ◽  
◽  
Kazuo Tanaka
Keyword(s):  
Time Delay ◽  
Controller Design ◽  
Fuzzy Model ◽  
Main Idea ◽  
Feedback Stabilization ◽  
Delay Systems ◽  
Control Synthesis ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Takagi Sugeno

In this paper, a class of nonlinear time-delay systems based on the Takagi-Sugeno (T-S) fuzzy model is defined. We investigate the delay-independent stability of this model. A model-based fuzzy stabilization design utilizing the concept of parallel distributed compensation (PDC) is employed. The main idea of the controller design is to derive each control rule to compensate each rule of a fuzzy system. Moreover, the problem of H∞ of this class of nonlinear time-delay systems is considered. The associated control synthesis problems are formulated as linear matrix inequality (LMI) problems.

Stability and control of fuzzy time delay systems with unmatched preconditions

2021 ◽  
pp. 1-13
Author(s):  
Yubao Hou ◽  
Jingding Gao
Keyword(s):  
Time Delay ◽  
Controller Design ◽  
Fuzzy Model ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
State Variables ◽  
Stability And Control ◽  
And Control ◽  
Fuzzy State

The stability and control of nonlinear time-delay systems of Takagi-Sugeno (T-S) fuzzy model are studied in this paper. The integral inequality of a free weight matrix is chosen to give a less conservative delay-dependent stability criterion in the form of linear matrix inequalities (LMIs). The premise mismatch strategy is applied, it is combined with Finsler lemma, a more flexible design method of fuzzy state feedback controller is proposed. This method does not require the controller and system to share the common premise membership function and the number of rules. The controller design strategy proposed in this paper can effectively solve the control problem of fuzzy systems when the number of state variables is not equal to the number of input variables (r≠c), or mi⁢(x⁢(t))≠hi⁢(x⁢(t)),i=1,2,…,r. Finally, two simulation examples are given to prove the advancement and effectiveness of the proposed theory.

scholarly journals Stability Analysis and Robust Stabilization of Uncertain Fuzzy Time-Delay Systems

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2441
Author(s):  
Chun-Tang Chao ◽  
Ding-Horng Chen ◽  
Juing-Shian Chiou
Keyword(s):  
Time Delay ◽  
Controller Design ◽  
Robust Stabilization ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Matrix Inequalities ◽  
Delay Dependent ◽  
Takagi Sugeno

New sufficient conditions for delay-independent and delay-dependent robust stability of uncertain fuzzy time-delay systems based on uncertain fuzzy Takagi-Sugeno (T-S) models are presented by using the properties of matrix and norm measurements. Further sufficient conditions are formulated, in terms of the linear matrix inequalities (LMIs) of robust stabilization, and are developed via the technique of parallel distributed compensation (PDC), and then the simplification of the conditions for the controller design of uncertain fuzzy time-delay systems. The proposed methods are simple and effective. Some examples below are presented to illustrate our results.

Sign in / Sign up

Export Citation Format

Share Document