H∞ control for a class of two-dimensional linear systems with fading measurements

2020 ◽  
pp. 014233122094462
Author(s):  
Wei Yu ◽  
Rui Wang ◽  
Xuhui Bu ◽  
Jiaqi Liang
Keyword(s):  
Closed Loop ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Two Dimensional ◽  
Closed Loop System ◽  
Discrete Time Systems ◽  
Control Schemes ◽  
Darboux Equation ◽  
Time Systems

In this paper, the [Formula: see text] control problem for a class of two-dimensional (2-D) linear discrete-time systems with fading measurements is investigated, where the 2-D systems are described by a Roesser model. The Rice fading model is applied to describe the fading phenomenon and the coefficients of the model satisfy the independent identical Gaussian distributions. The main objective of this paper is to design a controller such that both the 2-D closed-loop system is exponentially mean-square stable and the prescribed [Formula: see text] performance is guaranteed under the condition of applying the attenuation signals. By utilizing the Lyapunov stability theory and the linear matrix inequalities (LMIs) techniques, sufficient conditions are conducted to guarantee the desired tracking performance. Based on such conditions, the gain matrix of the proposed controller is obtained. Finally, the effectiveness of the proposed control schemes is illustrated with a numerical example and a Darboux equation example.

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

2009 ◽  
Vol 223 (6) ◽  
pp. 809-820 ◽  
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.

Stability and constrained control for positive two-dimensional systems with delays in the second FM model

2018 ◽  
Vol 36 (2) ◽  
pp. 515-536
Author(s):  
Jian Shen ◽  
Weiqun Wang
Keyword(s):  
Closed Loop ◽  
Sufficient Conditions ◽  
Multiple Delays ◽  
Two Dimensional ◽  
Bounded Control ◽  
Delayed Systems ◽  
Closed Loop Systems ◽  
The Stability ◽  
And Control ◽  
Time Systems

Abstract This paper addresses the stability and control problem of linear positive two-dimensional discrete-time systems with multiple delays in the second Fornasini–Marchesini model. The contribution lies in three aspects. First, a novel proof is provided to establish necessary and sufficient conditions of asymptotic stability for positive two-dimensional delayed systems. Then, a state-feedback controller is designed to ensure the non-negativity and stability of the closed-loop systems. Finally, a sufficient condition for the existence of constrained controllers is developed under the additional constraint of bounded control, which means that the control inputs and the states of the closed-loop systems are bounded. Two examples are given to validate the proposed methods.

Event-triggered Hꝏ control for NCS with time-delay and packet losses

2019 ◽  
Vol 37 (3) ◽  
pp. 918-934
Author(s):  
Jing Bai ◽  
Ying Wang ◽  
Li-Ying Zhao
Keyword(s):  
Time Delay ◽  
Closed Loop ◽  
Discrete Event ◽  
Sufficient Conditions ◽  
Loop System ◽  
Linear Matrix ◽  
Time Varying ◽  
Closed Loop System ◽  
Packet Losses ◽  
Event Triggered

Abstract This paper is concerned with the discrete event-triggered dynamic output-feedback ${H}_{\infty }$ control problem for the uncertain networked control system, where the time-varying sampling, network-induced delay and packet losses are taken into account simultaneously. The random packet losses are described via the Bernoulli distribution. And then, the closed-loop system is modelled as an augmented time-delay system with interval time-varying delay. By using the Lyapunov stability theory and the augmented state space method, the sufficient conditions for the asymptotic stability of the closed-loop system are proposed in the form of linear matrix inequalities. At the same time, the design method of the ${H}_{\infty }$ controller is created. Finally, a numerical example is employed to illustrate the effectiveness of the proposed method.

Output Feedback Algorithm for Nonlinear Systems with Compensation of Bounded Disturbances and Measurement Noises

2019 ◽  
Vol 20 (1) ◽  
pp. 3-15 ◽  
Author(s):  
I. B. Furtat ◽  
P. A. Gushchin ◽  
A. A. Peregudin
Keyword(s):  
Output Feedback ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Loop System ◽  
Partial Recovery ◽  
Closed Loop System ◽  
External Disturbances ◽  
Control Schemes ◽  
Measurement Noises ◽  
Feedback Algorithm

The output feedback algorithm for dynamic plants with compensation of parametric uncertainty, external disturbances and measurement noises is synthesized. The plants are described by a nonlinear system of differential equations with vector input and output signals. Unlike most existing control schemes in this paper the dimensions of the measurement interference and the output signal are equal, the sources of the signals of disturbances and disturbances are different, parametric and external disturbances can be present in any equation of the plant model. For simultaneous compensation of disturbances and measurement noises it is proposed to consider two channels. On the first channel a part of the measurement noises will be estimated which will allow partial recovery the information about the plant noisy output. On the second channel the disturbances will be compensated. Thus, at least two independent measurement channels are required for simultaneous compensation of disturbances and measurement noises. Sufficient conditions for calculating the parameters of the algorithm in the form of solvability of the linear matrix inequality are obtained. It is shown that the equation of a closed-loop system obtained on the basis of the proposed algorithm depends on the disturbances and the smallest component of the measurement noise. However, if the smallest component cannot be identified a priory, the results of the transients depend on the component of the noise that will be selected in the synthesis of the control system. Thus, unlike most existing control schemes, where the equation of a closed-loop system depends on disturbance and noise, the resulting algorithm provides better transients, because they do not depend on the entire noise vector, but only on its smallest (one) component. The simulations for a third-order nonlinear plant and the synchronization of an electrical generator connected to the power grid are presented. Numerical examples illustrate the effectiveness of the proposed scheme and the robustness with respect to random components in the noises and disturbances.

Robust nonfragile observer-based H2/H∞ controller

2016 ◽  
Vol 24 (4) ◽  
pp. 722-738 ◽  
Author(s):  
Atta Oveisi ◽  
Tamara Nestorović
Keyword(s):  
Control System ◽  
Real Time ◽  
Closed Loop ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Loop System ◽  
Linear Matrix ◽  
Closed Loop System ◽  
Real Time System ◽  
Structured Uncertainty

A robust nonfragile observer-based controller for a linear time-invariant system with structured uncertainty is introduced. The [Formula: see text] robust stability of the closed-loop system is guaranteed by use of the Lyapunov theorem in the presence of undesirable disturbance. For the sake of addressing the fragility problem, independent sets of time-dependent gain-uncertainties are assumed to be existing for the controller and the observer elements. In order to satisfy the arbitrary H2-normed constraints for the control system and to enable automatic determination of the optimal [Formula: see text] bound of the performance functions in disturbance rejection control, additional necessary and sufficient conditions are presented in a linear matrix equality/inequality framework. The [Formula: see text] observer-based controller is then transformed into an optimization problem of coupled set of linear matrix equalities/inequality that can be solved iteratively by use of numerical software such as Scilab. Finally, concerning the evaluation of the performance of the controller, the control system is implemented in real time on a mechanical system, aiming at vibration suppression. The plant under study is a multi-input single-output clamped-free piezo-laminated smart beam. The nominal mathematical reduced-order model of the beam with piezo-actuators is used to design the proposed controller and then the control system is implemented experimentally on the full-order real-time system. The results show that the closed-loop system has a robust performance in rejecting the disturbance in the presence of the structured uncertainty and in the presence of the unmodeled dynamics.

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

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.

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.

Exponentially Dissipative Control for Singular Impulsive Dynamical Systems

2017 ◽  
Vol 139 (4) ◽  
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.

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

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
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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