Design of delay observer-based controllers for uncertain time-lag systems

In this paper, the problem of designing observers and observer-based controllers for a class of uncertain systems with input and state time lags is considered. We construct delay-type observers in which both the instantaneous as well as the delayed measurements are utilized. Using feedback control based on the reconstructed state, the behavior of the closed-loop system is investigated. It is established that the uncertain time-lag system with delay observer-based control is asymptotically stable. Expressions for the gain matrices are given based on two linear-matrix inequalities. A numerical example is given to illustrate the theoretical developments.

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StochasticH∞Control for Discrete-Time Singular Systems with State and Disturbance Dependent Noise

Discrete Dynamics in Nature and Society ◽

10.1155/2017/4173852 ◽

2017 ◽

Vol 2017 ◽

pp. 1-10

Author(s):

Yong Zhao ◽

Xiushan Jiang ◽

Weihai Zhang

Keyword(s):

Discrete Time ◽

State Feedback ◽

Closed Loop ◽

Singular Systems ◽

State Feedback Control ◽

Linear Matrix ◽

Mean Square ◽

Matrix Inequalities ◽

Closed Loop System ◽

Theoretical Results

This paper is concerned with the stochasticH∞state feedback control problem for a class of discrete-time singular systems with state and disturbance dependent noise. Two stochastic bounded real lemmas (SBRLs) are proposed via strict linear matrix inequalities (LMIs). Based on the obtained SBRLs, a state feedbackH∞controller is presented, which not only guarantees the resulting closed-loop system to be mean square admissible but also satisfies a prescribedH∞performance level. A numerical example is finally given to illustrate the effectiveness of the proposed theoretical results.

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Vibration control of base-isolated structures using mixed H2/H∞ output-feedback control

Proceedings of the Institution of Mechanical Engineers Part I Journal of Systems and Control Engineering ◽

10.1243/09596518jsce730 ◽

2009 ◽

Vol 223 (6) ◽

pp. 809-820 ◽

Cited By ~ 5

Author(s):

H R Karimi ◽

M Zapateiro ◽

N Luo

Keyword(s):

Feedback Control ◽

Output Feedback ◽

Design Methodology ◽

Closed Loop ◽

Sufficient Conditions ◽

Output Feedback Control ◽

Linear Matrix ◽

Building Structures ◽

Matrix Inequalities ◽

Closed Loop System

A mixed H2/ H∞ output-feedback control design methodology for vibration reduction of base-isolated building structures modelled in the form of second-order linear systems is presented. Sufficient conditions for the design of a desired control are given in terms of linear matrix inequalities. A controller that guarantees asymptotic stability and a mixed H2/ H∞ performance for the closed-loop system of the structure is developed, based on a Lyapunov function. The performance of the controller is evaluated by means of simulations in MATLAB/Simulink.

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Observer-based sliding mode control for piezoelectric wing bending-torsion coupling flutter involving delayed output

Journal of Vibration and Control ◽

10.1177/1077546320949122 ◽

2020 ◽

pp. 107754632094912

Author(s):

Da Li ◽

Hui Yang ◽

Na Qi ◽

Jiaxin Yuan

Keyword(s):

Time Delay ◽

Sliding Mode Control ◽

Linear Matrix Inequalities ◽

Closed Loop ◽

Sliding Mode ◽

Loop System ◽

Linear Matrix ◽

Matrix Inequalities ◽

Closed Loop System ◽

Piezoelectric Patch

An observer-based sliding mode control scheme is proposed for suppressing bending-torsion coupling flutter motions of a wing aeroelastic system with delayed output by using the piezoelectric patch actuators. The wing structure is modeled as a thin-walled beam, and the aerodynamics on the wing are computed by the strip theory. For the implementation of the control algorithm, the piezoelectric patch is bonded on the top surface of the beam to act as the actuator. Ignoring the effect of piezoelectric actuators on structural dynamics, only considering the bending moments induced by piezoelectric effects, the corresponding dynamic motion equation is established by using the Lagrange method with the assumed mode method. The flutter speed and frequency of the closed-loop system with time delay are obtained by solving a polynomial eigenvalue problem. An observer-based controller that does not dependent on time delay is developed for suppressing the flutter, and the corresponding gain matrices are obtained by solving linear matrix inequalities. The sufficient condition for the asymptotic stability of the closed-loop system is derived in terms of linear matrix inequalities. The simulation results demonstrate that the proposed control strategy based on the piezoelectric actuator is effective in wing bending-torsion coupling flutter system with a delayed output.

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Robust H∞ Observer-Based Control Design for Discrete-Time Nonlinear Systems With Time-Varying Delay

WSEAS TRANSACTIONS ON SYSTEMS ◽

10.37394/23202.2021.20.11 ◽

2021 ◽

Vol 20 ◽

pp. 88-97

Author(s):

Mengying Ding ◽

Yali Dong

Keyword(s):

Nonlinear Systems ◽

Discrete Time ◽

Closed Loop ◽

Sufficient Conditions ◽

Linear Matrix ◽

Time Varying ◽

Matrix Inequalities ◽

Closed Loop System ◽

Time Varying Delay ◽

Varying Delay

This paper investigates the problem of robust H∞ observer-based control for a class of discrete-time nonlinear systems with time-varying delays and parameters uncertainties. We propose an observer-based controller. By constructing an appropriate Lyapunov-Krasovskii functional, some sufficient conditions are developed to ensure the closed-loop system is robust asymptotically stable with H∞ performance in terms of the linear matrix inequalities. Finally, a numerical example is given to illustrate the efficiency of proposed methods.

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Exponentially Dissipative Control for Singular Impulsive Dynamical Systems

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.4035166 ◽

2017 ◽

Vol 139 (4) ◽

Cited By ~ 1

Author(s):

Li Yang ◽

Xinzhi Liu ◽

Zhigang Zhang

Keyword(s):

Dynamical Systems ◽

Linear Matrix Inequalities ◽

State Feedback ◽

Closed Loop ◽

Sufficient Conditions ◽

Linear Matrix ◽

Matrix Inequalities ◽

Closed Loop System ◽

Dissipative Control ◽

Necessary And Sufficient

This paper studies the problem of exponentially dissipative control for singular impulsive dynamical systems. Some necessary and sufficient conditions for exponential dissipativity of such systems are established in terms of linear matrix inequalities (LMIs). A state feedback controller is designed to make the closed-loop system exponentially dissipative. A numerical example is given to illustrate the feasibility of the method.

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Robust Passivity Control for Uncertain Time-Delayed Systems

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.29-32.2025 ◽

2010 ◽

Vol 29-32 ◽

pp. 2025-2030

Author(s):

Gui Fang Li ◽

Yong Cheng Sun ◽

Sheng Guo Huang

Keyword(s):

Time Delay ◽

Closed Loop ◽

Passive Control ◽

Linear Time ◽

Linear Matrix ◽

Closed Loop System ◽

Parameter Uncertainties ◽

Delayed Systems ◽

Controller Gain ◽

Uncertain Time

This paper focuses on the robust passivity synthesis problem for a class of linear time-delayed systems subject to parameter uncertainties. The time delay is assumed to be unknown, and the parameter uncertainties are allowed to appear in all matrices of the model. The aim lies in designing observer-based dynamic controller that render the closed-loop system be strongly robustly stable and strict passive for all admissible uncertainties, independently of time delay. Using a scaling parameterization approach, the problem being considered is transformed into a class of strongly stable and strictly passive control problem for a parameterized system without uncertainties. And then, the controller gain and the observer gain are obtained in terms of a linear matrix inequality. Finally, a numerical example is provided to demonstrate the validity of the proposed approach.

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NonfragileH∞Control for Stochastic Systems with Markovian Jumping Parameters and Random Packet Losses

Abstract and Applied Analysis ◽

10.1155/2014/934134 ◽

2014 ◽

Vol 2014 ◽

pp. 1-8 ◽

Cited By ~ 1

Author(s):

Jing Wang ◽

Ke Zhang

Keyword(s):

Closed Loop ◽

Stochastic Systems ◽

Sufficient Conditions ◽

Linear Matrix ◽

Markovian Jumping Parameters ◽

Matrix Inequalities ◽

Closed Loop System ◽

Packet Losses ◽

Markovian Jumping ◽

Physical Plant

This paper is concerned with the nonfragileH∞control problem for stochastic systems with Markovian jumping parameters and random packet losses. The communication between the physical plant and controller is assumed to be imperfect, where random packet losses phenomenon occurs in a random way. Such a phenomenon is represented by a stochastic variable satisfying the Bernoulli distribution. The purpose is to design a nonfragile controller such that the resulting closed-loop system is stochastically mean square stable with a guaranteedH∞performance levelγ. By using the Lyapunov function approach, some sufficient conditions for the solvability of the previous problem are proposed in terms of linear matrix inequalities (LMIs), and a corresponding explicit parametrization of the desired controller is given. Finally, an example illustrating the effectiveness of the proposed approach is presented.

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Reliable Η∞ Control for Discrete-Time Switched Linear Systems with Intermittent Measurements

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.181-182.145 ◽

2011 ◽

Vol 181-182 ◽

pp. 145-150

Author(s):

Dong Sheng Du

Keyword(s):

Linear Systems ◽

Closed Loop ◽

Sufficient Conditions ◽

Linear Matrix ◽

Matrix Inequalities ◽

Closed Loop System ◽

Stochastic Variable ◽

Switched Linear Systems ◽

Stochastically Stable ◽

Intermittent Measurements

In this paper, a scheme of reliable control for switched linear systems with intermittent measurements is developed. The stochastic variable is assumed to be a Bernoulli distributed white sequence appearing in measured output. Sufficient conditions for the existence of the switched observer and the switched controller are derived in terms of linear matrix inequalities (LMIs), which can maintain the closed-loop system is stochastically stable with a prescribed performance level.

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

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.467.621 ◽

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.

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