scholarly journals New Criterion of Robust Hܣ Stabilization for Uncertain Neutral Systems

2021 ◽  
pp. 1-12
Author(s):  
Jiyong Lu
Keyword(s):  
Closed Loop ◽  
External Disturbance ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Asymptotically Stable ◽  
Neutral Systems ◽  
Closed Loop Systems ◽  
Delay Dependent ◽  
New Criterion ◽  
Robust Stability And Stabilization

The problems of delay-dependent robust stability and stabilization for a class of uncertain neutral systems are investigated in this paper. At first, by constructing a new Lyapunov functional and using the Lyapunov stability theory, a new delay-dependent condition which renders the system with no external disturbance and input to be asymptotically stable is obtained and given by a linear matrix inequality. Then, based on the obtained condition, a state feedback stabilize law is designed, which guarantees closed-loop neutral systems are asymptotically stable for all the permitted uncertainties when the external disturbance is naught, and it can also guarantee the closed-loop systems have  performance under the external disturbance. The model of neutral systems with both the uncertainty and the disturbance discussed in this paper has rarely been considered before.

Resilient anti-disturbance H∞ control for turbofan systems

2020 ◽  
Vol 42 (14) ◽  
pp. 2686-2697
Author(s):  
Yankai Li ◽  
Mou Chen ◽  
Tao Li ◽  
Huijiao Wang ◽  
Yu Kang
Keyword(s):  
Disturbance Observer ◽  
Closed Loop ◽  
Control Method ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Control Technique ◽  
Linear Matrix ◽  
Asymptotically Stable ◽  
Matrix Inequality ◽  
Closed Loop Systems

The problem of [Formula: see text] control is investigated for turbofan systems with uncertain parameters and multiple disturbances in this paper. Some disturbances with partly known information are described via an external system, and other disturbances are assumed to be [Formula: see text] norm bounded. According to the disturbance-observer-based-control (DOBC) method and resilient [Formula: see text] control technique, a robust resilient controller is designed to reject and attenuate the influence of these disturbances, and guarantees that closed-loop systems are asymptotically stable with [Formula: see text] performance. Some solvable sufficient conditions are obtained based on the linear matrix inequality (LMI) technique and Lyapunov stability theory. Finally, a simulation is presented to show the robustness and effectiveness of the developed resilient anti-disturbance [Formula: see text] control method.

A delay dependent approach to robust fast adaptive fault estimation design for uncertain neutral systems with time delay

2017 ◽  
Vol 40 (8) ◽  
pp. 2579-2588
Author(s):  
Hui Li ◽  
Fuqiang You ◽  
Fuli Wang
Keyword(s):  
Time Delay ◽  
External Disturbance ◽  
Fault Estimation ◽  
Linear Matrix ◽  
Asymptotically Stable ◽  
Matrix Inequality ◽  
Neutral Systems ◽  
Constant Delay ◽  
Schur Complements ◽  
Delay Dependent

This paper studies the problem of robust fault estimation for neutral systems, which is subjected to actuator fault, constant delay and norm bounded external disturbance. Based on the fast adaptive fault estimation (FAFE) algorithm, we focus on the design of fault estimation filter that guarantees the filtering error systems to be asymptotically stable with a prescribed [Formula: see text] performance. A novel Lyapunov-Krasovskii functional is employed, which includes the information of time delay. A delay dependent criterion of robust fault estimation design is obtained, and then the proposed result has advantages over some existing results, in that it has less conservatism and it enlarges the application scope. An improved sufficient condition for the existence of such a filter is proposed in terms of the linear matrix inequality (LMI) by the Schur complements and the cone complementary linearization algorithm. Finally, an illustrative example is given to show the effectiveness of the proposed method.

State Feedback Robust H∞ Control for Generalized Discrete System and Simulation

2013 ◽  
Vol 467 ◽  
pp. 621-626
Author(s):  
Chen Fang ◽  
Jiang Hong Shi ◽  
Kun Yu Li ◽  
Zheng Wang
Keyword(s):  
Discrete System ◽  
State Feedback ◽  
Closed Loop ◽  
The State ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
Robust Controller ◽  
Closed Loop Systems

For a class of uncertain generalized discrete linear system with norm-bounded parameter uncertainties, the state feedback robust control problem is studied. One sufficient condition for the solvability of the problem and the state feedback robust controller are obtained in terms of linear matrix inequalities. The designed controller guarantees that the closed-loop systems is regular, causal, stable and satisfies a prescribed norm bounded constraint for all admissible uncertain parameters under some conditions. The result of the normal discrete system can be regarded as a particular form of our conclusion. A simulation example is given to demonstrate the effectiveness of the proposed method.

DESIGN OF STATE ESTIMATOR FOR SWITCHED HOPFIELD NEURAL NETWORKS WITH TIME-DELAY

2011 ◽  
Vol 20 (04) ◽  
pp. 657-666
Author(s):  
CHOON KI AHN
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Estimation Error ◽  
Hopfield Neural Networks ◽  
Linear Matrix ◽  
Asymptotically Stable ◽  
State Estimator ◽  
Error System ◽  
Delay Dependent ◽  
Dependent State

In this paper, the delay-dependent state estimation problem for switched Hopfield neural networks with time-delay is investigated. Based on the Lyapunov–Krasovskii stability theory, a new delay-dependent state estimator for switched Hopfield neural networks is established to estimate the neuron states through available output measurements such that the estimation error system is asymptotically stable. The gain matrix of the proposed estimator is characterized in terms of the solution to a linear matrix inequality (LMI), which can be checked readily by using some standard numerical packages. An illustrative example is given to demonstrate the effectiveness of the proposed state estimator.

Design of H_/H∞ fault detection observer for closed-loop nonlinear system with disturbance

2020 ◽  
Vol 40 (4) ◽  
pp. 589-599
Author(s):  
Zhengquan Chen ◽  
Lu Han ◽  
Yandong Hou
Keyword(s):  
Fault Detection ◽  
Closed Loop ◽  
External Disturbance ◽  
Adaptive Threshold ◽  
Linear Matrix ◽  
Content Type ◽  
Non Linear ◽  
Runge Kutta ◽  
Non Linear System ◽  
Residual Generator

Purpose This paper proposes a novel method of fault detection, which is based on H_/H∞ Runge–Kutta observer and an adaptive threshold for a class of closed-loop non-linear systems. The purpose of this paper is to improve the rapidity and accuracy of fault detection. Design/methodology/approach First, the authors design the H_/H∞ Runge–Kutta fault detection observer, which is used as a residual generator to decouple the residual from the input. The H_ performance index metric in the specified frequency domain is used to describe how sensitive the residual to the fault. The H∞ norm is used to describe the residual robustness to the external disturbance of the systems. The residual generator is designed to achieve the best tradeoff between robustness against unknown disturbances but sensitivity to faults, thus realizing the accurate detection of the fault by suppressing the influence of noise and disturbance on the residual. Next, the design of the H_/H∞ fault detection observer is transformed into a convex optimization problem and solved by linear matrix inequality. Then, a new adaptive threshold is designed to improve the accuracy of fault detection. Findings The effectiveness and correctness of the method are tested in simulation experiments. Originality/value This paper presents a novel approach to improve the accuracy and rapidity of fault detection for closed-loop non-linear system with disturbances and noise.

Observer-Based Control of a Class of Switched Fuzzy Systems

2014 ◽  
Vol 945-949 ◽  
pp. 2539-2542
Author(s):  
Hong Yang ◽  
Huan Huan Lü ◽  
Le Zhang
Keyword(s):  
Fuzzy System ◽  
Fuzzy Systems ◽  
Function Method ◽  
State Feedback ◽  
Closed Loop ◽  
External Disturbance ◽  
Asymptotically Stable ◽  
Closed Loop System ◽  
Lyapunov Function Method ◽  
Switching State

For the non-measurable states, a control of switched fuzzy systems is presented based on observer. Using switching technique and multiple Lyapunov function method, the fuzzy observer is built to ensure that for all allowable external disturbance the relevant closed-loop system is asymptotically stable. Moreover, switching strategy achieving system global asymptotic stability of the switched fuzzy system is given. In this model, a switching state feedback controller is presented. A simulation shows the feasibility and the effectiveness of the method.

A New Approach to Delay-Dependent H∞ Control of Linear State-Delayed Systems

2004 ◽  
Vol 126 (1) ◽  
pp. 201-205 ◽  
Author(s):  
De-Jin Wang
Keyword(s):  
Controller Design ◽  
Linear Matrix ◽  
State Delay ◽  
Delayed Systems ◽  
Cross Term ◽  
Closed Loop Systems ◽  
Linear State ◽  
Delay Dependent ◽  
Time Invariant ◽  
Control Criterion

An alternative delay-dependent H∞ controller design is proposed for linear, continuous, time-invariant systems with unknown state delay. The resulting delay-dependent H∞ control criterion is obtained in terms of Park’s inequality for bounding cross term. The H∞ controller determined by a convex optimization algorithm with linear matrix inequality (LMI) constraints, guarantees the asymptotic stability of the closed-loop systems and reduces the effect of the disturbance input on the controlled output to within a prescribed level. A numerical example illustrates the effectiveness of our method.

scholarly journals A Novel Delay-Dependent Asymptotic Stability Conditions for Differential and Riemann-Liouville Fractional Differential Neutral Systems with Constant Delays and Nonlinear Perturbation

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 82 ◽  
Author(s):  
Watcharin Chartbupapan ◽  
Ovidiu Bagdasar ◽  
Kanit Mukdasai
Keyword(s):  
Asymptotic Stability ◽  
Stability Criterion ◽  
Nonlinear Perturbation ◽  
Linear Matrix ◽  
Neutral System ◽  
The Novel ◽  
Neutral Systems ◽  
Fractional Differential ◽  
Delay Dependent ◽  
Single Constant

The novel delay-dependent asymptotic stability of a differential and Riemann-Liouville fractional differential neutral system with constant delays and nonlinear perturbation is studied. We describe the new asymptotic stability criterion in the form of linear matrix inequalities (LMIs), using the application of zero equations, model transformation and other inequalities. Then we show the new delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral system with constant delays. Furthermore, we not only present the improved delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral system with single constant delay but also the new delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral equation with constant delays. Numerical examples are exploited to represent the improvement and capability of results over another research as compared with the least upper bounds of delay and nonlinear perturbation.

Stabilization of Fuzzy Markovian Jumping Systems with Distributed Delay

2014 ◽  
Vol 556-562 ◽  
pp. 4386-4390
Author(s):  
Zhao Ping Yuan
Keyword(s):  
Time Delay ◽  
Robust Stabilization ◽  
Distributed Delay ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Markovian Jumping ◽  
Weighting Matrix ◽  
Markovian Jumping Systems ◽  
Distributed Time Delay ◽  
Delay Dependent

This paper is concerned with the stabilization problem for fuzzy Markovian jumping systems with distributed time delay. First, fuzzy Markovian jumping systems with distributed time delay are peoposed. Second, a novel criterion of delay-dependent robust stabilization for fuzzy Markovian jumping systems is established in terms of linear matrix inequalities (LMIs) by using Lyapunov stability theory and free-weighting matrix method. When these LMIS are feasible, an explicit expression of a desired adjustable state feedback controller is given. Based on the obtained criterion, the introduced controller ensures the overall closed-loop system asymptotically stable in mean square sense for all admissible uncertainties and time delay.

scholarly journals Robust Moving HorizonH∞Control of Discrete Time-Delayed Systems with Interval Time-Varying Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
F. Yıldız Tascikaraoglu ◽  
I. B. Kucukdemiral ◽  
J. Imura
Keyword(s):  
Discrete Time ◽  
Disturbance Rejection ◽  
Closed Loop ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Time Varying ◽  
Discrete Time System ◽  
Delayed Systems ◽  
State Delays ◽  
Delay Dependent

In this study, design of a delay-dependent type moving horizon state-feedback control (MHHC) is considered for a class of linear discrete-time system subject to time-varying state delays, norm-bounded uncertainties, and disturbances with bounded energies. The closed-loop robust stability and robust performance problems are considered to overcome the instability and poor disturbance rejection performance due to the existence of parametric uncertainties and time-delay appeared in the system dynamics. Utilizing a discrete-time Lyapunov-Krasovskii functional, some delay-dependent linear matrix inequality (LMI) based conditions are provided. It is shown that if one can find a feasible solution set for these LMI conditions iteratively at each step of run-time, then we can construct a control law which guarantees the closed-loop asymptotic stability, maximum disturbance rejection performance, and closed-loop dissipativity in view of the actuator limitations. Two numerical examples with simulations on a nominal and uncertain discrete-time, time-delayed systems, are presented at the end, in order to demonstrate the efficiency of the proposed method.

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