scholarly journals Robust Impulsive Stabilization of Uncertain Nonlinear Singular Systems with Application to Transportation Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-4 ◽  
Author(s):  
Shaohong Fang
Keyword(s):  
Impulsive Control ◽  
Singular Systems ◽  
Singular System ◽  
Sufficient Conditions ◽  
Transportation Systems ◽  
Control Technique ◽  
Asymptotically Stable ◽  
Matrix Inequalities ◽  
Stabilization Problem ◽  
Uncertain Singular Systems

We consider the robust asymptotical stabilization problem for uncertain singular systems. We design a new impulsive control technique to ensure that the controlled singular system is robustly asymptotically stable and hence derive the corresponding stability criteria. These sufficient conditions are expressed in the form of algebra matrix inequalities and can be implemented numerically. We finally provide a numerical example of a transportation system to illustrate the effectiveness and usefulness of the proposed criteria.

Fault-Tolerant Control against Actuator Failures for a Class of Uncertain Singular Systems

2014 ◽  
Vol 539 ◽  
pp. 601-605 ◽  
Author(s):  
Guo Rong Wang ◽  
Juan Lei
Keyword(s):  
State Feedback ◽  
Fault Tolerant ◽  
Singular Systems ◽  
Singular System ◽  
Fault Tolerant Control ◽  
The State ◽  
Linear Matrix ◽  
Asymptotically Stable ◽  
Actuator Failures ◽  
Uncertain Singular Systems

In this paper, the fault-tolerant control problem for uncertain singular systems is discussed when actuator is normal and failure. First, using linear matrix inequalities (LMI), the state feedback is designed so that the singular system is asymptotically stable when the actuators work well. Then, the state feedback is designed so that the closed-loop singular system is asymptotically stable when the part actuators occur failure. Finally, the use of LMI method , the fault-tolerant state feedback controllers with integrity are presented for uncertain singular systems.

Robust PD State Feedback Controller Design for Uncertain Singular Systems

2011 ◽  
Vol 403-408 ◽  
pp. 3813-3818
Author(s):  
Jian Wu Zhu ◽  
Yuan Chun Ding
Keyword(s):  
State Feedback ◽  
Controller Design ◽  
Singular Systems ◽  
Sufficient Conditions ◽  
Feedback Controller ◽  
State Feedback Controller ◽  
Closed Loop Systems ◽  
Uncertain Singular Systems ◽  
Parameter Dependent ◽  
Robust Stability And Stabilization

This paper is concerned with the problem of robust stability and stabilization of singular systems with uncertainties in both the derivative and state matrices. By using a parameter dependent Lyapunov function, we derive the LMI-based sufficient conditions for the stabilization of the singular systems. Secondly, by solving these LMIs, a proportional plus derivative (PD) state feedback controller is designed for the closed-loop systems to be quadratically normal and quadratically stable (QNQS). Finally, the numerical example is given to show the effectiveness of the proposed theorems.

Further Results on Exponential Stability and State Feedback Stabilization for Time Delay Singular Saturating Actuator Systems With Delay-Dependence

2017 ◽  
Vol 139 (10) ◽  
Author(s):  
Pin-Lin Liu
Keyword(s):  
Time Delay ◽  
Convex Optimization ◽  
State Feedback ◽  
Singular Systems ◽  
Sufficient Conditions ◽  
Feedback Stabilization ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Decision Variables ◽  
Delay Dependence

This paper will study the exponential stable and state feedback stabilization of time delay singular systems with saturation actuators. Some sufficient conditions for existence of controller are obtained by using the linear matrix inequalities (LMIs) and integral inequality approach (IIA). When these LMIs are feasible, an explicit expression of controller is obtained. Based on Lyapunov–Krasovskii functional (LKF) techniques, a novel exponential stabilization criterion has been also derived in terms of LMIs which can be easily solved with efficient convex optimization algorithm. Our results are less conservative than some existing ones, and the decision variables involved in this paper are less than them. Examples illustrate our results as less conservative than those reported in the literature.

scholarly journals Stability Analysis and Robust H∞ Filtering for Discrete-time Nonlinear Systems with Time-varying Delays

2021 ◽  
Vol 20 ◽  
pp. 281-288
Author(s):  
Mengying Ding ◽  
Yali Dong
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Filter Design ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Asymptotically Stable ◽  
Matrix Inequalities ◽  
Error System ◽  
Error Dynamics

In this paper, we investigate the problem of robust H∞ filter design for a class of discrete-time nonlinear systems. The systems under consider involves time-varying delays and parameters uncertainties. The main objective is to design a linear full-order filter to ensure that the resulting filtering error system is asymptotically stable with a prescribed H∞ performance level. By constructing an appropriate Lyapunov-Krasovskii functional, some novel sufficient conditions are established to guarantee the filter error dynamics system is robust asymptotically stable with H∞ performance γ , and the H∞ filter is designed in term of linear matrix inequalities. Finally, a numerical example is provided to illustrate the efficiency of proposed method.

scholarly journals Model reduction design for continuous systems with finite frequency specifications

2021 ◽  
Vol 11 (5) ◽  
pp. 3956
Author(s):  
Miloud Koumir ◽  
Abderrahim El-Amrani ◽  
Ismail Boumhidi
Keyword(s):  
Model Reduction ◽  
Sufficient Conditions ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Continuous Systems ◽  
Asymptotically Stable ◽  
Matrix Inequalities ◽  
Finite Frequency ◽  
Error System ◽  
Takagi Sugeno

<p>This paper is concerned with the problem of model reduction design for continuous systems in Takagi-Sugeno fuzzy model. Through the defined FF H∞ gain performance, sufficient conditions are derived to design model reduction and to assure the fuzzy error system to be asymptotically stable with a FF H∞ gain performance index. The explicit conditions of fuzzy model reduction are developed by solving linear matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.</p>

scholarly journals Finite-Time Robust H∞ Control for Uncertain Linear Continuous-Time Singular Systems with Exogenous Disturbances

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Songlin Wo ◽  
Bo Li
Keyword(s):  
Continuous Time ◽  
Finite Time ◽  
Singular Systems ◽  
Singular System ◽  
Sufficient Conditions ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Exogenous Disturbance ◽  
Exogenous Disturbances ◽  
Definition Of

Singular systems arise in a great deal of domains of engineering and can be used to solve problems which are more difficult and more extensive than regular systems to solve. Therefore, in this paper, the definition of finite-time robust H∞ control for uncertain linear continuous-time singular systems is presented. The problem we address is to design a robust state feedback controller which can deal with the singular system with time-varying norm-bounded exogenous disturbance, such that the singular system is finite-time robust bounded (FTRB) with disturbance attenuation γ. Sufficient conditions for the existence of solutions to this problem are obtained in terms of linear matrix equalities (LMIs). When these LMIs are feasible, the desired robust controller is given. A detailed solving method is proposed for the restricted linear matrix inequalities. Finally, examples are given to show the validity of the methodology.

scholarly journals Stochastic Finite-Time Guaranteed Cost Control of Markovian Jumping Singular Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-20 ◽  
Author(s):  
Yingqi Zhang ◽  
Caixia Liu ◽  
Xiaowu Mu
Keyword(s):  
Finite Time ◽  
Cost Control ◽  
Transition Probabilities ◽  
Singular Systems ◽  
Singular System ◽  
Sufficient Conditions ◽  
Guaranteed Cost Control ◽  
Linear Matrix ◽  
Markovian Jumping ◽  
Guaranteed Cost

The problem of stochastic finite-time guaranteed cost control is investigated for Markovian jumping singular systems with uncertain transition probabilities, parametric uncertainties, and time-varying norm-bounded disturbance. Firstly, the definitions of stochastic singular finite-time stability, stochastic singular finite-time boundedness, and stochastic singular finite-time guaranteed cost control are presented. Then, sufficient conditions on stochastic singular finite-time guaranteed cost control are obtained for the family of stochastic singular systems. Designed algorithms for the state feedback controller are provided to guarantee that the underlying stochastic singular system is stochastic singular finite-time guaranteed cost control in terms of restricted linear matrix equalities with a fixed parameter. Finally, numerical examples are given to show the validity of the proposed scheme.

Robust State-Feedback Controller Design for Uncertainty Singular Systems

2011 ◽  
Vol 383-390 ◽  
pp. 32-37
Author(s):  
Li Ming Liang ◽  
Fa Lu Weng ◽  
Yuan Chun Ding
Keyword(s):  
Controller Design ◽  
Singular Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Robust Controller ◽  
Uncertain Singular Systems ◽  
Stability And Stabilization ◽  
The Stability ◽  
Parameter Dependent ◽  
Robust Stability And Stabilization

In this paper the problem of robust stability and stabilization of a class of uncertain singular Systems with uncertainties in both the derivative and state matrices is studied. By using a parameter dependent Lyapunov function, we derive the linear matrix inequalities (LMIs) based sufficient conditions for the stability and stabilization of the system. By solving these LMIs, the robust controller is derived. Finally, the numerical example is given to show the effectiveness of the proposed theorems.

Asymptotic Stability Analysis and Controller Design for a Class of Switched Uncertain Singular Systems with Time-Delay

2013 ◽  
Vol 385-386 ◽  
pp. 890-895
Author(s):  
Yue Sheng Luo ◽  
Shan Gao ◽  
Yang Gao ◽  
Tong Li ◽  
Chun Fang Liu
Keyword(s):  
Time Delay ◽  
Asymptotic Stability ◽  
Lyapunov Function ◽  
Controller Design ◽  
Singular Systems ◽  
Singular System ◽  
Equivalent Transformation ◽  
Switching Law ◽  
Uncertain Singular Systems ◽  
Delay Dependent

The problem of robustly asymptotic stability and controller design for a class of switched uncertain singular systems with time-delay is considered. By means of Lyapunov function and Matrix equivalent transformation, based on multiple Lyapunov function techniques, a delay-dependent sufficient condition is deduced, such that the solution of the switched singular system with time-delay is robustly asymptotic stable for all admissible uncertainties under an appropriate switching law. Furthermore, a convex optimization problem with LMI constraints is formulated such that the maximum bound on the admissible delay can be determined by using the LMI toolbox in MATLAB. Finally, an illustrative example is given to demonstrate the effectiveness of proposed method.

Robust Control of Uncertain Singular Systems with Distributed Delays

2013 ◽  
Vol 457-458 ◽  
pp. 856-860
Author(s):  
Yan Bo Li ◽  
Bi Rong Li
Keyword(s):  
Robust Control ◽  
Integral Inequality ◽  
Model Transformation ◽  
State Feedback ◽  
Singular Systems ◽  
Lyapunov Functionals ◽  
Asymptotically Stable ◽  
Uncertain Singular Systems ◽  
Inequality Technique ◽  
Linear State

Robust control for a class of singular systems with distributed delaysand uncertainties is researched. Firstly, a linear state-feedback controller isdesigned. Secondly, without model transformation and matrices decomposition, Asufficient condition for the studied systems, which makes sure the systems tobe regular, impulse free and asymptotically stable, is given by constructingthe appropriate Lyapunov functionals in terms of linear matrixinequalities(LMIs) method and integral inequality technique. The obtained results can be shown in LMIs andsovled easily by LMI toolbox in Matlab. At last, A numerical example is givento illustrate the validity of the method

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