Tracking of Periodic Trajectories for Switched Systems Under Time-Varying Asynchronous Switching

2019 ◽  
Vol 141 (8) ◽  
Author(s):  
Guoqi Ma ◽  
Xinghua Liu ◽  
Prabhakar R. Pagilla ◽  
Shuzhi Sam Ge
Keyword(s):  
Output Feedback ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Dynamic Output Feedback ◽  
Time Varying ◽  
Decomposition Approach ◽  
Dynamic Output ◽  
2D Model ◽  
Repetitive Controller

In this technical brief, we provide an asynchronous modified repetitive controller design to address the periodic trajectory tracking problem for switched systems with time-varying switching delays between plant modes and controllers. In the feedback channel, a dynamic output feedback mechanism is adopted. By utilizing the lifting technique, the dynamic output feedback-based switched repetitive control system is transformed into a continuous-discrete two-dimensional (2D) model to differentiate the control and learning actions involved in the repetitive controller. For the transformed 2D model, by constructing a piecewise Lyapunov functional and utilizing a matrix decomposition approach, sufficient conditions in terms of linear matrix inequalities (LMIs) and the average dwell time are developed to guarantee closed-loop exponential stability. The performance of the proposed approach is illustrated via a switched RLC series circuit example and numerical simulations are provided.

Asynchronous repetitive control of switched systems via periodic event-based dynamic output feedback

2019 ◽  
Vol 37 (2) ◽  
pp. 644-673
Author(s):  
Guoqi Ma ◽  
Xinghua Liu ◽  
Prabhakar R Pagilla ◽  
Shuzhi Sam Ge
Keyword(s):  
Output Feedback ◽  
Switched Systems ◽  
Closed Loop ◽  
Repetitive Control ◽  
Mode Switching ◽  
Dynamic Output Feedback ◽  
Time Varying ◽  
Design Framework ◽  
Dynamic Output ◽  
Event Based

Abstract This paper develops an asynchronous mode-dependent repetitive control strategy with periodic event-based dynamic output feedback for periodic trajectory tracking of continuous-time switched systems subject to time-varying switching delays between system modes and controllers and limited communication capacity in the feedback channel. By employing the input delay approach, the overall system is modelled as an augmented closed-loop switched system with both constant and time-varying state delays. A co-design framework is proposed for simultaneously designing the controller, event-triggering mechanism and mode switching signal. Under the co-design framework, using piecewise Lyapunov functional, free-weighting matrices and average dwell time technique, sufficient conditions are derived for ensuring the augmented closed-loop system to be exponentially stable with a prescribed $H_{\infty }$ attenuation level $\gamma $ for an exogenous disturbance input. The performance of the proposed controller design scheme is verified via numerical simulation results on a switched RLC series circuit system.

scholarly journals Non-fragile dynamic output feedback H∞ control for a class of uncertain switched systems with time-varying delay

2021 ◽  
Vol 3 (1) ◽  
Author(s):  
Yuning Song ◽  
Yuzhong Liu
Keyword(s):  
Output Feedback ◽  
Linear Matrix ◽  
Dynamic Output Feedback ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Dynamic Output ◽  
Nonlinear Matrix Inequality ◽  
Nonlinear Matrix ◽  
Varying Delay

The problem of non-fragile dynamic output feedback H∞ control for a class of uncertain switched systems with time-varying delay is discussed. Firstly, the form of non-fragile dynamic output feedback H∞ controller is given. Under the condition that the upper bound of time delay and the upper bound of delay derivative are limited simultaneously, Lyapunov functional and its corresponding switching rules are constructed by using single Lyapunov function method and convex combination technique; Secondly, we use the inequality lemma to scale the derived Lyapunov functional in order to eliminate the time-varying delay term in the inequality, and then introduce the J-function to obtain a nonlinear matrix inequality that satisfies the H∞ performance index γ, we also employ Schur complement lemma to transform the nonlinear matrix inequality into set of linear matrix inequalities consisting of two linear matrix inequalities, a sufficient condition for the existence of a non-fragile dynamic output feedback H∞ controller and satisfying the H∞ performance index γ is concluded for a class of uncertain switching systems with variable time delay; Finally, a switched system composed of two subsystems is considered and the effectiveness and practicability of the theorem are illustrated by numerical simulation with LMI toolbox. 

scholarly journals Dynamic Output Feedback Control of Discrete Markov Jump Systems based on Event-Triggered Mechanism

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Zhen Zhao ◽  
Jinfeng Gao ◽  
Tingting Zhang
Keyword(s):  
Time Delay ◽  
Output Feedback ◽  
Sufficient Conditions ◽  
Output Feedback Control ◽  
Linear Matrix ◽  
Dynamic Output Feedback ◽  
Markov Jump ◽  
System A ◽  
Dynamic Output ◽  
Event Triggered

This paper is devoted to the co-design strategy of event-triggered scheme and dynamic output feedback controller for a class of discrete-time networked control systems (NCSs) with random time delay. An event-triggered mechanism is given to ease the information transmission. Both the sensor and controller are set with mode-dependent quantizers in the system. A Markov process is used to model the time delay which is used to describe the quantization density. By employing the Lyapunov-Krasovskii functional and linear matrix inequality (LMI), sufficient conditions are obtained for the system. A specific example is given to demonstrate the proposed approach.

scholarly journals Exponential Admissibility and Dynamic Output Feedback Control of Switched Singular Systems with Interval Time-Varying Delay

2010 ◽  
Vol 2010 ◽  
pp. 1-21 ◽  
Author(s):  
Jinxing Lin ◽  
Chunxia Fan
Keyword(s):  
Output Feedback ◽  
Singular Systems ◽  
Delay System ◽  
Linear Matrix ◽  
Dynamic Output Feedback ◽  
Time Varying ◽  
Interval Time ◽  
Time Varying Delay ◽  
Dynamic Output ◽  
Varying Delay

This paper is concerned with the problems of exponential admissibility and dynamic output feedback (DOF) control for a class of continuous-time switched singular systems with interval time-varying delay. A full-order, dynamic, synchronously switched DOF controller is considered. First, by using the average dwell time approach, a delay-range-dependent exponential admissibility criterion for the unforced switched singular time-delay system is established in terms of linear matrix inequalities (LMIs). Then, based on this criterion, a sufficient condition on the existence of a desired DOF controller, which guarantees that the closed-loop system is regular, impulse free and exponentially stable, is proposed by employing the LMI technique. Finally, some illustrative examples are given to show the effectiveness of the proposed approach.

Adaptive H∞ Power and Rate Control for Time-Varying Uncertain Wireless Networks via Dynamic Output Feedback

2014 ◽  
Vol 548-549 ◽  
pp. 1524-1529
Author(s):  
Cun Wu Han ◽  
De Hui Sun ◽  
Zhi Jun Li ◽  
Yun Tao Shi
Keyword(s):  
Wireless Networks ◽  
Output Feedback ◽  
Rate Control ◽  
Control Technique ◽  
Linear Matrix ◽  
Dynamic Output Feedback ◽  
Time Varying ◽  
Control Approach ◽  
Dynamic Output ◽  
Rate Control Algorithm

This paper investigates power and rate control for wireless networks with time-varying uncertainties. A new power and rate control algorithm via dynamic output feedback is presented based on adaptive control technique and robust H∞ control approach. The adaptive H∞ performance of the closed-loop system is analyzed based on the linear matrix inequality (LMI). Simulation results are given to demonstrate the effectiveness of the proposed controller.

Finite-time dynamic output feedback stabilization of linear time-varying systems by a piecewise constant method

2018 ◽  
Vol 40 (14) ◽  
pp. 4078-4088
Author(s):  
Chao Liang ◽  
Chenxiao Cai ◽  
Jing Xu
Keyword(s):  
Output Feedback ◽  
Finite Time ◽  
Linear Time ◽  
Dynamic Output Feedback ◽  
Time Varying ◽  
Piecewise Constant ◽  
Output Feedback Controller ◽  
Dynamic Output ◽  
Time Varying Systems ◽  
Dynamic Output Feedback Controller

The paper mainly deals with the problem of finite-time stabilization of linear time-varying systems. A dynamic output feedback controller is designed, which is able to stabilize the linear time-varying systems in finite time. By virtue of extended piecewise constant method, novel criteria for the existence of a dynamic output feedback controller is established in terms of linear matrix inequalities. Compared with the existing method, the proposed method is more efficient from a computational point of view. A simulation is given to illustrate the effectiveness of the obtained result.

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