scholarly journals Nonfragile Robust Finite-TimeL2-L∞Controller Design for a Class of Uncertain Lipschitz Nonlinear Systems with Time-Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Jun Song ◽  
Shuping He
Keyword(s):  
Finite Time ◽  
Time Delays ◽  
Controller Design ◽  
Linear Matrix ◽  
Nonlinear Parameters ◽  
Lipschitz Nonlinear Systems ◽  
Exogenous Disturbances ◽  
Nonlinear Uncertain Systems ◽  
The Given ◽  
Lipschitz Conditions

The nonfragile robust finite-timeL2-L∞control problem for a class of nonlinear uncertain systems with uncertainties and time-delays is considered. The nonlinear parameters are considered to satisfy the Lipschitz conditions and the exogenous disturbances are unknown but energy bounded. By using the Lyapunov function approach, the sufficient condition for the existence of nonfragile robust finite-timeL2-L∞controller is given in terms of linear matrix inequalities (LMIs). The finite-time controller is designed such that the resulting closed-loop system is finite-time bounded for all admissible uncertainties and satisfies the givenL2-L∞control index. Simulation results illustrate the validity of the proposed approach.

A finite-time H-infinite adaptive fault-tolerant controller considering time delay for flutter suppression of airfoil flutter

2019 ◽  
Vol 234 (2) ◽  
pp. 293-307
Author(s):  
Gao Ming-Zhou ◽  
Chen Xin-Yi ◽  
Han Rong ◽  
Yao Jian-Yong
Keyword(s):  
Finite Time ◽  
Control Method ◽  
Controller Design ◽  
Fault Tolerant ◽  
Linear Matrix ◽  
Control Methods ◽  
Actuator Faults ◽  
Control Delay ◽  
Modeling Uncertainties ◽  
The Stability

To suppress airfoil flutter, a lot of control methods have been proposed, such as classical control methods and optimal control methods. However, these methods did not consider the influence of actuator faults and control delay. This paper proposes a new finite-time H∞ adaptive fault-tolerant flutter controller by radial basis function neural network technology and adaptive fault-tolerant control method, taking into account actuator faults, control delay, modeling uncertainties, and external disturbances. The theoretic section of this paper is about airfoil flutter dynamic modeling and adaptive fault-tolerant controller design. Lyapunov function and linear matrix inequality are employed to prove the stability of the proposed control method of this paper. The numeral simulation section further proves the effectiveness and robustness of the proposed control algorithm of this paper.

scholarly journals Resilient Robust Finite-TimeL2-L∞Controller Design for Uncertain Neutral System with Mixed Time-Varying Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Xia Chen ◽  
Shuping He
Keyword(s):  
Finite Time ◽  
State Feedback ◽  
Controller Design ◽  
Linear Matrix ◽  
Neutral System ◽  
Time Varying ◽  
Constraint Condition ◽  
Closed Loop System ◽  
Delayed System ◽  
Delay Dependent

The delay-dependent resilient robust finite-timeL2-L∞control problem of uncertain neutral time-delayed system is studied. The disturbance input is assumed to be energy bounded and the time delays are time-varying. Based on the Lyapunov function approach and linear matrix inequalities (LMIs) techniques, a state feedback controller is designed to guarantee that the resulted closed-loop system is finite-time bounded for all uncertainties and to satisfy a givenL2-L∞constraint condition. Simulation results illustrate the validity of the proposed approach.

Finite-time guaranteed cost controller design for uncertain linear continuous-time singular systems

2019 ◽  
Vol 41 (12) ◽  
pp. 3507-3515 ◽  
Author(s):  
Bo Li ◽  
Songlin Wo ◽  
Junjie Zhao ◽  
Xuejing Ren
Keyword(s):  
Continuous Time ◽  
Finite Time ◽  
Closed Loop ◽  
Controller Design ◽  
Singular Systems ◽  
Singular System ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Guaranteed Cost ◽  
Bounded Uncertainties

This article concerns the finite-time robust guaranteed cost control problem for a class of linear continuous-time singular systems with norm-bounded uncertainties. In this study, the problem is to design a state feedback controller such that the closed-loop system is finite-time stable, and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties. By constructing an appropriate Lyapunov function, a sufficient condition for the finite-time robust stability of the system based on linear matrix inequality (LMI) is established. Furthermore, the sufficient condition for the existence of the guaranteed cost controller is formulated in terms of LMIs, which can make the closed-loop uncertain singular system finite-time robust stable. Finally, two numerical examples are given for illustration of the proposed theoretical results.

scholarly journals Finite-Time Robust H∞ Control for Uncertain Linear Continuous-Time Singular Systems with Exogenous Disturbances

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Songlin Wo ◽  
Bo Li
Keyword(s):  
Continuous Time ◽  
Finite Time ◽  
Singular Systems ◽  
Singular System ◽  
Sufficient Conditions ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Exogenous Disturbance ◽  
Exogenous Disturbances ◽  
Definition Of

Singular systems arise in a great deal of domains of engineering and can be used to solve problems which are more difficult and more extensive than regular systems to solve. Therefore, in this paper, the definition of finite-time robust H∞ control for uncertain linear continuous-time singular systems is presented. The problem we address is to design a robust state feedback controller which can deal with the singular system with time-varying norm-bounded exogenous disturbance, such that the singular system is finite-time robust bounded (FTRB) with disturbance attenuation γ. Sufficient conditions for the existence of solutions to this problem are obtained in terms of linear matrix equalities (LMIs). When these LMIs are feasible, the desired robust controller is given. A detailed solving method is proposed for the restricted linear matrix inequalities. Finally, examples are given to show the validity of the methodology.

Finite-Time Stabilization for Singular Linear Time-Delay Systems with Time-Varying Exogenous Disturbance

2012 ◽  
Vol 490-495 ◽  
pp. 2459-2463 ◽  
Author(s):  
Min Su ◽  
Shu Wei Wang ◽  
Xian Zhang
Keyword(s):  
Time Delay ◽  
Finite Time ◽  
Linear Time ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Delay Systems ◽  
Exogenous Disturbance ◽  
Exogenous Disturbances ◽  
Finite Time Stabilization

In this paper finite-time stabilization for singular linear time-delay systems with time-varying exogenous disturbances is defined. By combining Lyapunov approach and matrix inequality technique, a sufficient condition of the finite-time stabilization for this kind of systems is presented by a set of feasible problems involving linear matrix inequalities (LMIs) with nonlinear constraints. In addition, the nonlinear feasible problems are solved by an so-called cone complementary linearization (CCL) algorithm. The effectiveness of the approach proposed in this paper is presented by a numerical example.

Finite-time passive filtering for a class of neutral time-delayed systems

2016 ◽  
Vol 39 (8) ◽  
pp. 1139-1145 ◽  
Author(s):  
Xia Chen ◽  
Shuping He
Keyword(s):  
Finite Time ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Combined System ◽  
Delayed Systems ◽  
Finite Time Stability ◽  
Functional Methods ◽  
Exogenous Disturbances ◽  
Error System ◽  
Filtering Problem

In this paper, the finite-time passive filtering problem of a class of neutral time-delayed systems is considered. The exogenous disturbances are unknown but norm bounded. A sufficient condition for passivity and finite-time stability of the combined system is derived and proved by means of Lyapunov functional methods and linear matrix inequalities (LMIs) techniques. The dynamic of the filtering error system is ensured to be finite-time bounded with a prescribed dissipation performance level [Formula: see text]. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.

scholarly journals Finite-Time Admissibility and Controller Design for T-S Fuzzy Stochastic Singular Systems with Distinct Differential Term Matrices

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Liang Qiao ◽  
Zhaomin Lv
Keyword(s):  
Finite Time ◽  
Stochastic Systems ◽  
Controller Design ◽  
Design Method ◽  
Singular Systems ◽  
Linear Matrix ◽  
Fuzzy Membership Functions ◽  
Fuzzy Lyapunov Function ◽  
Parameter Perturbations ◽  
Stochastic Singular Systems

The finite-time admissibility analysis and controller design issues for extended T-S fuzzy stochastic singular systems (FSSSs) with distinct differential term matrices and Brownian parameter perturbations are discussed. When differential term matrices are allowed to be distinct in fuzzy rules, such fuzzy models can describe a wide class of nonlinear stochastic systems. Using fuzzy Lyapunov function (FLF), a new and relaxed sufficient condition is proposed via strict linear matrix inequalities (LMIs). Different from the existing stability conditions by FLF, the derivative bounds of fuzzy membership functions are not required in this condition. Based on admissibility analysis results, a design method for parallel distribution compensation (PDC) controller of FSSSs is given to guarantee the finite-time admissibility of the closed-loop system. Finally, the feasibility and effectiveness of the proposed methods in this article are illustrated with three examples.

scholarly journals Finite-Time Control of Singular Linear Semi-Markov Jump Systems

Algorithms ◽  
2021 ◽  
Vol 15 (1) ◽  
pp. 8
Author(s):  
Xiaofu Ji ◽  
Xuehua Liu
Keyword(s):  
Finite Time ◽  
Controller Design ◽  
External Disturbance ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Markov Jump ◽  
Markov Jump Systems ◽  
One Dimensional ◽  
Time Control ◽  
Jump Systems

The problem of finite-time control for singular linear semi-Markov jump systems (SMJSs) with unknown transition rates is considered in this paper. By designing a new semi-positive definite Lyapunov-like function, state feedback controller design methods are given that allow closed-loop singular linear SMJSs to be regular, impulse-free and stochastically finite-time-stable without external disturbance, and stochastically finite-time bounded with external disturbance. The obtained conditions are expressed by a set of strict matrix inequalities, which can be simplified to a set of linear matrix inequalities by a one dimensional search for a scalar. Two numerical examples are given to illustrate the effectiveness of proposed method.

scholarly journals Neural Network Based Finite-Time Stabilization for Discrete-Time Markov Jump Nonlinear Systems with Time Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Fei Chen ◽  
Fei Liu ◽  
Hamid Reza Karimi
Keyword(s):  
Neural Networks ◽  
Nonlinear Systems ◽  
Discrete Time ◽  
Finite Time ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Space Representation ◽  
Linear Matrix ◽  
Markov Jump ◽  
Finite Time Stabilization

This paper deals with the finite-time stabilization problem for discrete-time Markov jump nonlinear systems with time delays and norm-bounded exogenous disturbance. The nonlinearities in different jump modes are parameterized by neural networks. Subsequently, a linear difference inclusion state space representation for a class of neural networks is established. Based on this, sufficient conditions are derived in terms of linear matrix inequalities to guarantee stochastic finite-time boundedness and stochastic finite-time stabilization of the closed-loop system. A numerical example is illustrated to verify the efficiency of the proposed technique.

scholarly journals LMI based control design for linear systems with distributed time delays

2012 ◽  
Vol 22 (2) ◽  
pp. 217-231 ◽  
Author(s):  
Anna Filasová ◽  
Daniel Gontkovič ◽  
Dušan Krokavec
Keyword(s):  
Linear Systems ◽  
Time Delays ◽  
Controller Design ◽  
Control Design ◽  
System Structure ◽  
Linear Matrix ◽  
Extended Form ◽  
Structured Matrix ◽  
Distributed Time Delays ◽  
Time Linear

LMI based control design for linear systems with distributed time delaysThe paper concerns the problem of stabilization of continuous-time linear systems with distributed time delays. Using extended form of the Lyapunov-Krasovskii functional candidate, the controller design conditions are derived and formulated with respect to the incidence of structured matrix variables in the linear matrix inequality formulation. The result give sufficient condition for stabilization of the system with distributed time delays. It is illustrated with a numerical example to note reduced conservatism in the system structure.

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