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.

Sliding Mode H∞-Control with Stochastic Time Delay Systems

2013 ◽  
Vol 321-324 ◽  
pp. 1712-1718
Author(s):  
Ravi Kumar ◽  
Kil To Chong
Keyword(s):  
Time Delay ◽  
Sliding Mode ◽  
Estimation Error ◽  
Sufficient Conditions ◽  
Feedback Stabilization ◽  
Delay Systems ◽  
Linear Matrix ◽  
Linear Filter ◽  
Time Delay Systems ◽  
Stochastic Time

In this paper, we concerned the problem of sliding mode of-control with stochastic stabilization of uncertainty. Some sufficient conditions are derived for this class of robust feedback stabilization of time delay systems. The stochastic time delay systems may switch from one to one corresponds of linear filter, such that the dynamics of estimation error is guaranteed to be stochastically stable in mean square. Moreover, it is shown that for a class of special linear stochastic neutral systems, the H-sliding mode control design can be obtained by solving linear matrix inequalities (LMIs).

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.

scholarly journals T-S Fuzzy Model-Based Approximation and Filter Design for Stochastic Time-Delay Systems with Hankel Norm Criterion

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Yanhui Li ◽  
Xiujie Zhou
Keyword(s):  
Time Delay ◽  
Filter Design ◽  
Fuzzy Model ◽  
Lyapunov Stability Theory ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Hankel Norm ◽  
Error System ◽  
Stochastic Time

This paper investigates the Hankel norm filter design problem for stochastic time-delay systems, which are represented by Takagi-Sugeno (T-S) fuzzy model. Motivated by the parallel distributed compensation (PDC) technique, a novel filtering error system is established. The objective is to design a suitable filter that guarantees the corresponding filtering error system to be mean-square asymptotically stable and to have a specified Hankel norm performance levelγ. Based on the Lyapunov stability theory and the Itô differential rule, the Hankel norm criterion is first established by adopting the integral inequality method, which can make some useful efforts in reducing conservativeness. The Hankel norm filtering problem is casted into a convex optimization problem with a convex linearization approach, which expresses all the conditions for the existence of admissible Hankel norm filter as standard linear matrix inequalities (LMIs). The effectiveness of the proposed method is demonstrated via a numerical example.

scholarly journals RobustH∞Control for a Class of Uncertain Switched Fuzzy Time-Delay Systems Based on T-S Models

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Yang Cui ◽  
Kaiqing Liu ◽  
Yang Zhao ◽  
Xue Wang
Keyword(s):  
Time Delay ◽  
Closed Loop ◽  
Design Method ◽  
Fuzzy Model ◽  
Delay Systems ◽  
Linear Matrix ◽  
Stable Theory ◽  
Time Delay Systems ◽  
Switching Law ◽  
Continuous State

The problem of robustH∞control for a class of uncertain switched fuzzy time-delay systems is discussed for system described by T-S fuzzy model with Lyapunov stable theory and linear matrix inequality approach. A sufficient condition in terms of the LMI is derived such that the stability of the closed-loop systems is guaranteed. The continuous state feedback controller is built to ensure the asymptotically stable closed-loop system for all allowable uncertainties, with the switching law designed to implement the global asymptotic stability of uncertain switched fuzzy time-delay systems. In this model, each and every subsystem of the switched systems is an uncertain fuzzy one to which the parallel distributed compensation (PDC) controller of each sub fuzzy system system is proposed with its main condition given in a more solvable form of convex combinations. Such a switched control system is highly robust to varying parameters. A simulation shows the feasibility and effectiveness of the design method.

Application of Fuzzy H∞ Control via T–S Fuzzy Models for Nonlinear Time-Delay Systems

2003 ◽  
Vol 12 (02) ◽  
pp. 117-137 ◽  
Author(s):  
Feng-Hsiag Hsiao ◽  
Wei-Ling Chiang
Keyword(s):  
Time Delay ◽  
Fuzzy Controller ◽  
Controller Design ◽  
Direct Method ◽  
Delay System ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Fuzzy Controllers ◽  
Fuzzy Models ◽  
Takagi Sugeno

This paper deals with the problem of stability analysis and stabilization via Takagi-Sugeno (T-S) fuzzy models for nonlinear time-delay systems. First, Takagi-Sugeno (T-S) fuzzy models and some stability results are recalled. To design fuzzy controllers, nonlinear time-delay systems are represented by Takagi-Sugeno fuzzy models. The concept of parallel-distributed compensation (PDC) is employed to determine structures of fuzzy controllers from the T-S fuzzy models. LMI-based design problems are defined and employed to find feedback gains of fuzzy controller and common positive definite matrices P satisfying stability a delay-dependent stability criterion derived in terms of Lyapunov direct method. Based on the control scheme and this criterion, a fuzzy controller is then designed via the technique of PDC to stabilize the nonlinear time-delay system and the H∞ control performance is achieved in the mean time. Finally, the proposed controller design method is demonstrated through numerical simulations on the chaotic and resonant systems.

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.

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