scholarly journals Resilient Robust Finite-TimeL2-L∞Controller Design for Uncertain Neutral System with Mixed Time-Varying Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Xia Chen ◽  
Shuping He
Keyword(s):  
Finite Time ◽  
State Feedback ◽  
Controller Design ◽  
Linear Matrix ◽  
Neutral System ◽  
Time Varying ◽  
Constraint Condition ◽  
Closed Loop System ◽  
Delayed System ◽  
Delay Dependent

The delay-dependent resilient robust finite-timeL2-L∞control problem of uncertain neutral time-delayed system is studied. The disturbance input is assumed to be energy bounded and the time delays are time-varying. Based on the Lyapunov function approach and linear matrix inequalities (LMIs) techniques, a state feedback controller is designed to guarantee that the resulted closed-loop system is finite-time bounded for all uncertainties and to satisfy a givenL2-L∞constraint condition. Simulation results illustrate the validity of the proposed approach.

scholarly journals Improved Results on Delay-Dependent Robust H ∞ Control of Uncertain Neutral Systems with Mixed Time-Varying Delays

2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Jingsha Zhang ◽  
Yongke Li ◽  
Xiaolin Ma ◽  
Zhilong Lin ◽  
Changlong Wang
Keyword(s):  
State Feedback ◽  
Controller Design ◽  
The State ◽  
Linear Matrix ◽  
Feedback Gain ◽  
Time Varying ◽  
Neutral Systems ◽  
The Matrix ◽  
Left And Right ◽  
Delay Dependent

In this paper, the problem of the delay-dependent robust H ∞ control for a class of uncertain neutral systems with mixed time-varying delays is studied. Firstly, a robust delay-dependent asymptotic stability criterion is shown by linear matrix inequalities (LMIs) after introducing a new Lyapunov–Krasovskii functional (LKF). The LKF including vital terms is expected to obtain results of less conservatism by employing the technique of various efficient convex optimization algorithms and free matrices. Then, based on the obtained criterion, analyses for uncertain systems and H ∞ controller design are presented. Moreover, on the analysis of the state-feedback controller, different from the traditional method which multiplies the matrix inequality left and right by some matrix and its transpose, respectively, we can obtain the state-feedback gain directly by calculating the LMIs through the toolbox of MATLAB in this paper. Finally, the feasibility and validity of the method are illustrated by examples.

State feedback observer-based control design for linear descriptor systems with multiple time-varying delays

2020 ◽  
Vol 37 (4) ◽  
pp. 1218-1236
Author(s):  
V N Phat ◽  
P Niamsup ◽  
N H Muoi
Keyword(s):  
State Feedback ◽  
Design Method ◽  
Sufficient Conditions ◽  
Descriptor Systems ◽  
Linear Matrix ◽  
Multiple Time ◽  
Time Varying ◽  
Feedback Controllers ◽  
Delay Function ◽  
Delay Dependent

Abstract In this paper, we propose an linear matrix inequality (LMI)-based design method to observer-based control problem of linear descriptor systems with multiple time-varying delays. The delay function can be continuous and bounded but not necessarily differentiable. First, by introducing a new set of improved Lyapunov–Krasovskii functionals that avoid calculating the derivative of the delay function, we obtain new delay-dependent sufficient conditions for guaranteeing the system to be regular, impulse-free and asymptotically stable. Then, based on the derived stability conditions, we design state feedback controllers and observer gains via LMIs, which can be solved numerically in standard computational algorithms. A numerical example with simulation is given to demonstrate the efficiency and validity of the proposed deign.

Fault-Distribution Dependent Reliable H∞ Control for Takagi-Sugeno Fuzzy Systems

2014 ◽  
Vol 136 (2) ◽  
Author(s):  
R. Sakthivel ◽  
P. Vadivel ◽  
K. Mathiyalagan ◽  
A. Arunkumar
Keyword(s):  
Fuzzy Systems ◽  
State Feedback ◽  
Linear Matrix ◽  
Closed Loop System ◽  
Actuator Failure ◽  
Time Varying Delay ◽  
Actuator Failures ◽  
Delay Dependent ◽  
Takagi Sugeno ◽  
Varying Delay

This paper is concerned with the problem of robust reliable H∞ control for a class of uncertain Takagi-Sugeno (TS) fuzzy systems with actuator failures and time-varying delay. The main objective is to design a state feedback reliable H∞ controller such that, for all admissible uncertainties as well as actuator failure cases, the resulting closed-loop system is robustly asymptotically stable with a prescribed H∞ performance level. Based on the Lyapunov-Krasovskii functional (LKF) method together with linear matrix inequality (LMI) technique, a delay dependent sufficient condition is established in terms of LMIs for the existence of robust reliable H∞ controller. When these LMIs are feasible, a robust reliable H∞ controller can be obtained. Finally, two numerical examples with simulation result are utilized to illustrate the applicability and effectiveness of our obtained result.

scholarly journals Finite-Time Passivity and Passification Design for Markovian Jumping Systems with Mode-Dependent Time-Varying Delays

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Chao Ma
Keyword(s):  
Finite Time ◽  
Functional Method ◽  
Linear Matrix ◽  
Time Varying ◽  
Markovian Jumping ◽  
Markovian Jumping Systems ◽  
The Mean ◽  
Delay Dependent ◽  
Passivity And Passification ◽  
Theoretical Results

This paper investigates the finite-time passivity and passification design problem for a class of Markovian jumping systems with mode-dependent time-varying delays. By employing the Lyapunov-Krasovskii functional method, delay-dependent sufficient criteria are derived to ensure the mean-square stochastically finite-time passivity. Based on the established results, mode-dependent passification controller is further designed in terms of linear matrix inequalities, such that the prescribed passive performance index of the resulting closed-loop system can be satisfied. Finally, two illustrative examples are given to show the effectiveness of the obtained theoretical results.

Positive Finite-Time Stabilization for Discrete-Time Linear Systems

2014 ◽  
Vol 137 (1) ◽  
Author(s):  
Wenping Xue ◽  
Kangji Li
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Finite Time ◽  
State Feedback ◽  
Closed Loop ◽  
Linear Matrix ◽  
Closed Loop System ◽  
Initial State ◽  
Finite Time Stability ◽  
Time Linear

In this paper, a new finite-time stability (FTS) concept, which is defined as positive FTS (PFTS), is introduced into discrete-time linear systems. Differently from previous FTS-related papers, the initial state as well as the state trajectory is required to be in the non-negative orthant of the Euclidean space. Some test criteria are established for the PFTS of the unforced system. Then, a sufficient condition is proposed for the design of a state feedback controller such that the closed-loop system is positively finite-time stable. This condition is provided in terms of a series of linear matrix inequalities (LMIs) with some equality constraints. Moreover, the requirement of non-negativity of the controller is considered. Finally, two examples are presented to illustrate the developed theory.

H∞ State-Feedback Control for Semi-Markov Jump Linear Systems With Time-Varying Delays

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Ji Huang ◽  
Yang Shi
Keyword(s):  
Linear Systems ◽  
State Feedback ◽  
Controller Design ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Time Varying ◽  
Markov Jump ◽  
Jump Linear Systems ◽  
Markov Jump Linear Systems

Semi-Markov jump linear systems (S-MJLSs) are more general than Markov jump linear systems in modeling practical systems. This paper investigates the H∞ control problem for a class of semi-Markov jump linear systems with time-varying delays. The sojourn-time partition technique is firstly proposed for the delayed stochastic switching system. A sufficient condition for designing the state feedback controller is then established. Moreover, the sufficient condition is expressed as a set of linear matrix inequalities which can be readily solved. A numerical example illustrates the effectiveness of the proposed controller design technique.

scholarly journals New Results on Reachable Set Estimation and Controller Design for Linear Systems with Mixed Delays via Triple Integral Functionals

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Wei Kang ◽  
Shouming Zhong
Keyword(s):  
Linear Systems ◽  
State Feedback ◽  
Controller Design ◽  
Reachable Set ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Closed Loop System ◽  
Set Estimation ◽  
Reachable Set Estimation ◽  
Bounded Disturbance

This paper is concerned with the problem of reachable set estimation and controller design for a class of linear systems with mixed delays and bounded disturbance inputs. By constructing a newly augmented Lyapunov-Krasovskii functional, combining with triple integral technique and reciprocally convex approach, some new reachable set estimation conditions are derived in terms of linear matrix inequalities. Based on these conditions, a state-feedback controller has been designed to ensure the reachable set of the closed-loop system bounded by a given ellipsoid. Finally, two numerical examples are given to illustrate the effectiveness of the proposed analysis and designed method.

A Novel Delay-Independent Robust Adaptive Controller Design for Uncertain Nonlinear Systems With Time-Varying State Delay

2019 ◽  
Vol 15 (1) ◽  
Author(s):  
Hadi Azmi ◽  
Alireza Yazdizadeh
Keyword(s):  
Nonlinear Systems ◽  
Linear Matrix Inequality ◽  
Closed Loop ◽  
Controller Design ◽  
Loop System ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
System Delay ◽  
Closed Loop System

Abstract In this paper, two novel adaptive control strategies are presented based on the linear matrix inequality for nonlinear Lipschitz systems. The proposed approaches are developed by creatively using Krasovskii stability theory to compensate parametric uncertainty, unknown time-varying internal delay, and bounded matched or mismatched disturbance effects in closed-loop system of nonlinear systems. The online adaptive tuning controllers are designed such that reference input tracking and asymptotic stability of the closed-loop system are guaranteed. A novel structural algorithm is developed based on linear matrix inequality (LMI) and boundaries of the system delay or uncertainty. The capabilities of the proposed tracking and regulation methods are verified by simulation of three physical uncertain nonlinear system with real practical parameters subject to internal or state time delay and disturbance.

scholarly journals Robust Reliable Stabilization of Switched Nonlinear Systems with Time-Varying Delays and Delayed Switching

2010 ◽  
Vol 2010 ◽  
pp. 1-21 ◽  
Author(s):  
Zhengrong Xiang ◽  
Qingwei Chen
Keyword(s):  
Nonlinear Systems ◽  
State Feedback ◽  
Linear Matrix ◽  
Time Varying ◽  
Switched Nonlinear Systems ◽  
Matrix Inequalities ◽  
Closed Loop System ◽  
Parameter Uncertainties ◽  
Actuator Failure ◽  
Exponentially Stable

This paper is concerned with the problem of robust reliable stabilization of switched nonlinear systems with time-varying delays and delayed switching is investigated. The parameter uncertainties are allowed to be norm-bounded. The switching instants of the controller experience delays with respect to those of the system. The purpose of this problem is to design a reliable state feedback controller such that, for all admissible parameter uncertainties and actuator failure, the system state of the closed-loop system is exponentially stable. We show that the addressed problem can be solved by means of algebraic matrix inequalities. The explicit expression of the desired robust controllers is derived in terms of linear matrix inequalities (LMIs).

scholarly journals Further Results Concerning Delay-DependentH∞Control for Uncertain Discrete-Time Systems with Time-Varying Delay

2009 ◽  
Vol 2009 ◽  
pp. 1-24 ◽  
Author(s):  
Guangdeng Zong ◽  
Linlin Hou ◽  
Hongyong Yang
Keyword(s):  
Discrete Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Closed Loop System ◽  
Parameter Uncertainties ◽  
Time Varying Delay ◽  
Discrete Time Systems ◽  
Delay Dependent ◽  
Time Systems ◽  
Varying Delay

This paper addresses the problem ofH∞control for uncertain discrete-time systems with time-varying delays. The system under consideration is subject to time-varying norm-bounded parameter uncertainties in both the state and controlled output. Attention is focused on the design of a memoryless state feedback controller, which guarantees that the resulting closed-loop system is asymptotically stable and reduces the effect of the disturbance input on the controlled output to a prescribed level irrespective of all the admissible uncertainties. By introducing some slack matrix variables, new delay-dependent conditions are presented in terms of linear matrix inequalities (LMIs). Numerical examples are provided to show the reduced conservatism and lower computational burden than the previous results.

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