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.

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.

Delay-dependent robust H∞ control for neutral time-delay systems

2014 ◽  
Vol 24 (5) ◽  
Author(s):  
MAN SUN ◽  
AIMIN YANG
Keyword(s):  
Time Delay ◽  
Performance Criterion ◽  
Controller Synthesis ◽  
Delay Systems ◽  
Descriptor System ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Matrix Inequalities ◽  
Delay Dependent ◽  
Decoupled Structure

We derive a delay-dependent H∞ performance criterion with a decoupled structure for systems with neutral time delay. We then extend it to an H∞ controller synthesis for systems with polytopic uncertainty. All conditions are given in terms of linear matrix inequalities (LMIs). In some previous descriptor system methods, the products of the controller and Lyapunov matrices are completely separated for the performance analysis, but not for controller synthesis - the method developed in the current paper eliminates this weakness. We present a numerical example to illustrate the effectiveness of the solution.

H∞ Constrained Pareto Suboptimal Strategy for Stochastic LPV Time-Delay Systems

2021 ◽  
pp. 2150010
Author(s):  
Hiroaki Mukaidani ◽  
Hua Xu ◽  
Weihua Zhuang
Keyword(s):  
Time Delay ◽  
Dynamic Games ◽  
Sufficient Conditions ◽  
Existence Condition ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Matrix Inequalities ◽  
Bounded Real Lemma ◽  
State Delays

Not only in control problems, but also in dynamic games, several sources of performance degradation, such as model variation, deterministic and stochastic uncertainties and state delays, need to be considered. In this paper, we present an [Formula: see text] constrained Pareto suboptimal strategy for stochastic linear parameter-varying (LPV) time-delay systems involving multiple decision makers. The goal of developing the [Formula: see text] constrained Pareto suboptimal strategy set is to construct a memoryless state feedback strategy set, so that the closed-loop stochastic LPV system is stochastically mean-square stable. In the paper, the existence condition of the extended bounded real lemma is first established via linear matrix inequalities (LMIs). Then, a quadratic cost bound for cost performance is derived. Based on these preliminary results, sufficient conditions for the existence of such a strategy set under the [Formula: see text] constraint are derived by using cross-coupled bilinear matrix inequalities (BMIs). To determine the strategy set, a viscosity iterative scheme based on the LMIs is established to avoid the processing of BMIs. Finally, two numerical examples are presented to demonstrate the reliability and usefulness of the proposed method.

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.

Robust H∞ Control of Time-Delay Systems

2013 ◽  
Vol 634-638 ◽  
pp. 3849-3852
Author(s):  
Man Sun
Keyword(s):  
Time Delay ◽  
State Feedback ◽  
Performance Criterion ◽  
Delay Systems ◽  
Linear Matrix ◽  
Polytopic Uncertainty ◽  
Time Delay Systems ◽  
Matrix Inequalities ◽  
Feedback Synthesis ◽  
Delay Dependent

In this paper, a delay-dependent H_infinity performance criterion which possess decoupling structure is derived for a class of time-delay systems. It is then extended to H_infinity state-feedback synthesis for time-delay systems with polytopic uncertainty. All the conditions are given in terms of the linear matrix inequalities (LMIs). Numerical examples illustrate the effectiveness of our methods.

scholarly journals Delay-DependentH∞Filtering for Singular Time-Delay Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-20 ◽  
Author(s):  
Zhenbo Li ◽  
Shuqian Zhu
Keyword(s):  
Time Delay ◽  
Delay Systems ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Time Delay Systems ◽  
Matrix Inequalities ◽  
Error System ◽  
Cone Complementarity Linearization ◽  
Delay Dependent ◽  
Singular Time

This paper deals with the problem of delay-dependentH∞filtering for singular time-delay systems. First, a new delay-dependent condition which guarantees that the filter error system has a prescribedH∞performanceγis given in terms of linear matrix inequalities (LMIs). Then, the sufficient condition is obtained for the existence of theH∞filter, and the explicit expression for the desiredH∞filter is presented by using LMIs and the cone complementarity linearization iterative algorithm. A numerical example is provided to illustrate the effectiveness of the proposed method.

scholarly journals New delay-dependent observer-based control for uncertain stochastic time-delay systems

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Xiu-feng Miao ◽  
Long-suo Li
Keyword(s):  
Time Delay ◽  
The State ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Parameter Uncertainties ◽  
Noise Disturbances ◽  
System States ◽  
Delay Dependent ◽  
Stochastic Time

AbstractThis paper considers the problem of estimating the state vector of uncertain stochastic time-delay systems, while the system states are unmeasured. The system under study involves parameter uncertainties, noise disturbances and time delay, and they are dependent on the state. Based on the Lyapunov–Krasovskii functional approach, we present a delay-dependent condition for the existence of a state observer in terms of a linear matrix inequality. A numerical example is exploited to show the validity of the results obtained.

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.

Passive Control for Uncertain Stochastic Time-Delay Systems

2011 ◽  
Vol 58-60 ◽  
pp. 691-696
Author(s):  
Cheng Wang ◽  
Huan Bin Liu
Keyword(s):  
Time Delay ◽  
Passive Control ◽  
Stochastic Systems ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Time Varying Delay ◽  
Delay Dependent ◽  
And Control ◽  
Stochastic Time

This paper investigates the problems of delay-dependent passive analysis and control for uncertain stochastic systems with time-varying delay and norm-bounded parameters uncertainties. Delay-dependent stochastic passive condition for the uncertain stochastic time-delay systems is obtained based on Laypunov-Krasovkii functional approach. On the basis of this condition, a delay-dependent passive controller is presented. Sufficient condition for the existence of desired controller is formulated in terms of linear matrix inequality. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

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