Finite-time H∞ synchronization of semi-Markov jump Lur’e systems

2021 ◽  
pp. 2150168
Author(s):  
Xin Huang ◽  
Youmei Zhou ◽  
Muyun Fang ◽  
Jianping Zhou ◽  
Sabri Arik
Keyword(s):  
Finite Time ◽  
State Feedback ◽  
Time Synchronization ◽  
Control Method ◽  
Design Method ◽  
External Disturbance ◽  
Feedback Controller ◽  
Markov Jump ◽  
Lur’E Systems ◽  
State Feedback Controller

This paper investigates the problem of finite-time [Formula: see text] synchronization for semi-Markov jump Lur’e systems with time-varying delay and external disturbance. The purpose of this work is to design a mode-dependent state-feedback controller to ensure that the synchronization-error system achieves finite-time synchronization with a prescribed [Formula: see text] performance index. A criterion for the finite-time synchronization is proposed by using appropriate Lyapunov functional and two recently developed inequalities. Then, a design method for the required state-feedback controller is presented with the application of several decoupling techniques. Finally, an example is provided to illustrate the applicability of the proposed control method.

scholarly journals Robust Position Control of a Two-Sided 1-DoF Impacting Mechanical Oscillator Subject to an External Persistent Disturbance by Means of a State-Feedback Controller

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Firas Turki ◽  
Hassène Gritli ◽  
Safya Belghith
Keyword(s):  
State Feedback ◽  
Position Control ◽  
External Disturbance ◽  
Feedback Controller ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Mechanical Oscillator ◽  
Impact Oscillator ◽  
State Feedback Controller ◽  
The Impact

This paper proposes a state-feedback controller using the linear matrix inequality (LMI) approach for the robust position control of a 1-DoF, periodically forced, impact mechanical oscillator subject to asymmetric two-sided rigid end-stops. The periodic forcing input is considered as a persistent external disturbance. The motion of the impacting oscillator is modeled by an impulsive hybrid dynamics. Thus, the control problem of the impact oscillator is recast as a problem of the robust control of such disturbed impulsive hybrid system. To synthesize stability conditions, we introduce the S-procedure and the Finsler lemmas by only considering the region within which the state evolves. We show that the stability conditions are first expressed in terms of bilinear matrix inequalities (BMIs). Using some technical lemmas, we convert these BMIs into LMIs. Finally, some numerical results and simulations are given. We show the effectiveness of the designed state-feedback controller in the robust stabilization of the position of the impact mechanical oscillator under the disturbance.

scholarly journals Finite-Time Synchronization of Singular Hybrid Coupled Networks

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Cong Zheng ◽  
Jinde Cao
Keyword(s):  
Finite Time ◽  
Stability Theory ◽  
State Feedback ◽  
Time Synchronization ◽  
Singular Systems ◽  
Sufficient Conditions ◽  
Feedback Controller ◽  
Time Stability ◽  
Finite Time Stability ◽  
Coupled Networks

This paper investigates finite-time synchronization of the singular hybrid coupled networks. The singular systems studied in this paper are assumed to be regular and impulse-free. Some sufficient conditions are derived to ensure finite-time synchronization of the singular hybrid coupled networks under a state feedback controller by using finite-time stability theory. A numerical example is finally exploited to show the effectiveness of the obtained results.

Global Lagged Finite-Time Synchronization of Two Chaotic Lur’e Systems Subject to Time Delay

2015 ◽  
Vol 25 (12) ◽  
pp. 1550161 ◽  
Author(s):  
Yun Chen ◽  
Xiaofeng Wu ◽  
Qian Lin
Keyword(s):  
Time Delay ◽  
Finite Time ◽  
Time Synchronization ◽  
Signal Transmission ◽  
Feedback Controller ◽  
Linear Matrix ◽  
Lur’E Systems ◽  
Chaotic Lur’E Systems ◽  
Variable Substitution ◽  
Synchronization Scheme

This paper investigates the global lagged finite-time synchronization of the master-slave Lur’e systems subject to time delay of signal transmission. By designing a variable-substitution and feedback controller, a master-slave finite-time synchronization scheme for the Lur’e systems with time delay is built up. Two delay-independent global lagged finite-time synchronization criteria are proved in the forms of linear matrix inequalities (LMIs), and the corresponding settling time of synchronization is analytically estimated. The obtained LMI criteria are applied to Chua’s oscillators, obtaining some easily implemented algebraic criteria under various single-variable-substitution and feedback controller, which are then optimized to improve their conservative property. Finally, several numerical examples are illustrated to verify the effectiveness of the optimized criteria.

scholarly journals Finite-Time Control of Networked Control Systems with Time Delay and Packet Dropout

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Yerong Sun ◽  
Yeguo Sun ◽  
Chunzhi Yang
Keyword(s):  
Control System ◽  
Time Delay ◽  
Control Theory ◽  
Control Systems ◽  
Finite Time ◽  
State Feedback ◽  
Network Control ◽  
Feedback Controller ◽  
Network Control System ◽  
State Feedback Controller

This paper studies the finite-time stabilization and boundedness problem of a class of network control systems that are simultaneously affected by time delay and packet loss. Based on the Lyapunov function method, the sufficient conditions for the design of the state feedback controller in the form of linear matrix inequality are obtained. The state feedback controller makes the network control system stable for a finite time. Finally, a numerical example is given to illustrate the effectiveness and feasibility of the method. The research results of this paper will develop and enrich the control theory system of the network control system and provide advanced control theory methods and application technology reserves in order to promote the development process of the network control system application and improve the application level.

Finite-Time Control for Switched Discrete-Time System

2013 ◽  
Vol 313-314 ◽  
pp. 516-523
Author(s):  
Wei Ming Xiang ◽  
Yong Chi Zhao
Keyword(s):  
Discrete Time ◽  
Finite Time ◽  
State Feedback ◽  
Average Dwell Time ◽  
Feedback Controller ◽  
Time Interval ◽  
Discrete Time System ◽  
State Feedback Controller ◽  
Fast Switching ◽  
Slow Switching

Finite-time stability concerns the boundless of system during a fixed finite-time interval. In this paper, the problem of finite-time stabilization for switched discrete-time systems is addressed. Both the fast switching and slow switching case are considered. In fast switching case, the designed state feedback controller combines controllers for each subsystem and resetting controller at switching instant, it is shown that the resetting controller can reduce the conservativeness on controller design. Under slow switching, state feedback controller is designed with admissible average dwell time. Several numerical examples are given to illustrate the proposed results within this paper.

State feedback stabilization for nonlinear systems with more general high-order terms

2018 ◽  
Vol 41 (3) ◽  
pp. 615-620
Author(s):  
Tiancheng Wang ◽  
Shi Zheng ◽  
Wuquan Li
Keyword(s):  
Nonlinear Systems ◽  
State Feedback ◽  
Design Method ◽  
High Order ◽  
The State ◽  
Feedback Stabilization ◽  
Feedback Controller ◽  
Closed Loop System ◽  
Globally Asymptotically Stable ◽  
State Feedback Controller

This paper aims to solve the state feedback stabilization problem for a class of high-order nonlinear systems with more general high-order terms. Based on the backstepping design method and Lyapunov stability theorem, a state feedback controller is constructed to ensure that the origin of the closed-loop system is globally asymptotically stable. The efficiency of the state feedback controller is demonstrated by a simulation example.

scholarly journals Finite-Time Control for Markovian Jump Systems with Polytopic Uncertain Transition Description and Actuator Saturation

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Zhongyi Tang
Keyword(s):  
Finite Time ◽  
State Feedback ◽  
Actuator Saturation ◽  
Feedback Controller ◽  
Markovian Jump Systems ◽  
Time Interval ◽  
Markovian Jump ◽  
State Feedback Controller ◽  
Attenuation Level ◽  
Jump Systems

The problem of finite-timeL2-L∞control for Markovian jump systems (MJS) is investigated. The systems considered time-varying delays, actuator saturation, and polytopic uncertain transition description. The purpose of this paper is to design a state feedback controller such that the system is finite-time bounded (FTB) and a prescribedL2-L∞disturbance attenuation level during a specified time interval is guaranteed. Based on the Lyapunov method, a linear matrix inequality (LMI) optimization problem is formulated to design the delayed feedback controller which satisfies the given attenuation level. Finally, illustrative examples show that the proposed conditions are effective for the design of robust state feedback controller.

Robust Control for Networked Control Systems With Admissible Parameter Uncertainties

2005 ◽  
Author(s):  
Kun Ji ◽  
Won-Jong Kim
Keyword(s):  
Control Systems ◽  
Time Delays ◽  
State Feedback ◽  
Controller Design ◽  
Networked Control Systems ◽  
Design Method ◽  
Feedback Controller ◽  
Dynamic State ◽  
Parameter Uncertainties ◽  
State Feedback Controller

In this paper, robust H∞ control problems for networked control systems (NCSs) with network-induced time delays and subject to norm-bounded parameter uncertainties are presented and solved. Based on a new discrete-time model, two approaches of robust controller design are proposed—design of a memoryless state-feedback controller and design of a dynamic state-feedback controller. The proposed memoryless state-feedback controller design method is given in terms of linear matrix inequalities (LMIs), and the delay bound can be computed by using the standard LMI techniques. A numerical example is given to illustrate the feasibility and effectiveness of this methodology. The proposed dynamic state-feedback controller design method is based on a discrete-time Artstein transform. With the sufficient conditions for robust stability and H∞ control developed in this paper, we also derive the upper bound of network-induced time delays and the lower bound of the network date-transmission rate that can be used as a guideline in choosing proper networks as communication media for NCSs. We constructed an NCS test bed to experimentally verify the feasibility and effectiveness of proposed design methodologies.

Sign in / Sign up

Export Citation Format

Share Document