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.

Non-Fragile Guaranteed Cost Control for a Class of Uncertain Time-Delay Switched Singular Systems

2013 ◽  
Vol 380-384 ◽  
pp. 639-647
Author(s):  
Yue Sheng Luo ◽  
Man Xu ◽  
Shi Lei Zhang ◽  
Tong Li ◽  
Chun Fang Liu
Keyword(s):  
Time Delay ◽  
Cost Control ◽  
Singular Systems ◽  
Singular System ◽  
Guaranteed Cost Control ◽  
Feasibility Problem ◽  
Linear Matrix ◽  
Cost Index ◽  
Guaranteed Cost ◽  
Uncertain Time

The problem of robustly non-fragile guaranteed cost control for a class of uncertain time-delay switched singular systems under arbitrary switching laws is considered. By means of matrix equivalent transformation and the relationship between the norm and the matrix, based on linear matrix inequality tools, a sufficient condition on the existence of non-fragile guaranteed cost state feedback controllers is derived, which ensures that uncertain time-delay switched singular system is admissible, and a corresponding cost index can be guaranteed. The design problem of the non-fragile guaranteed cost controller can be turned into the feasibility problem of a set of linear matrix inequalities. Finally, an illustrative example is given to demonstrate the effectiveness of proposed method.

Guaranteed Cost Control for Fuzzy Bilinear Systems with Uncertain Parameters

2012 ◽  
Vol 433-440 ◽  
pp. 1723-1729
Author(s):  
Ze Feng Gao ◽  
Jun Chen ◽  
Fei Liu
Keyword(s):  
Cost Control ◽  
Fuzzy Controller ◽  
Sufficient Conditions ◽  
Schur Complement ◽  
Guaranteed Cost Control ◽  
Bilinear Systems ◽  
Linear Matrix ◽  
Main Theme ◽  
Control Laws ◽  
Guaranteed Cost

The main theme of this paper is to present robust guaranteed cost control laws for a class of fuzzy bilinear systems (FBS) with parametric uncertainties. First, the piecewise Lyapunov function (PLF) method is utilized to design a fuzzy controller, which ensures the robust asymptotic stability of the closed-loop system, and then the robust guaranteed cost control law is also proposed. Second, based on the Schur complement and some variable transformations, some sufficient conditions are derived to guarantee the stability of the overall fuzzy control system via linear matrix inequalities (LMIs). Finally, a numerical example is utilized to demonstrate the validity and effectiveness of the proposed control scheme.

Finite-time guaranteed cost controller design for uncertain linear continuous-time singular systems

2019 ◽  
Vol 41 (12) ◽  
pp. 3507-3515 ◽  
Author(s):  
Bo Li ◽  
Songlin Wo ◽  
Junjie Zhao ◽  
Xuejing Ren
Keyword(s):  
Continuous Time ◽  
Finite Time ◽  
Closed Loop ◽  
Controller Design ◽  
Singular Systems ◽  
Singular System ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Guaranteed Cost ◽  
Bounded Uncertainties

This article concerns the finite-time robust guaranteed cost control problem for a class of linear continuous-time singular systems with norm-bounded uncertainties. In this study, the problem is to design a state feedback controller such that the closed-loop system is finite-time stable, and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties. By constructing an appropriate Lyapunov function, a sufficient condition for the finite-time robust stability of the system based on linear matrix inequality (LMI) is established. Furthermore, the sufficient condition for the existence of the guaranteed cost controller is formulated in terms of LMIs, which can make the closed-loop uncertain singular system finite-time robust stable. Finally, two numerical examples are given for illustration of the proposed theoretical results.

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.

Guaranteed cost finite-time control of large-scale singular systems with interconnected delays

2021 ◽  
pp. 014233122110471
Author(s):  
Pham T Huong ◽  
Vu N Phat
Keyword(s):  
Finite Time ◽  
Large Scale ◽  
Singular Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Decomposition Approach ◽  
Time Control ◽  
Guaranteed Cost ◽  
Value Decomposition ◽  
Delay Dependent

The guaranteed cost finite-time control problem of large-scale singular systems subjected to interconnected state delays is addressed in this article. A singular value decomposition approach combining with the Lyapunov function method is proposed to study the problem. Based on the method, delay-dependent sufficient conditions are established to design guaranteed cost controllers, which are presented in terms of tractable linear matrix inequalities. An example with simulation is given to demonstrate the validity and effectiveness of the theoretical results.

Resilient Guaranteed Cost Control for Singular Systems with Time-Varying Interval Delay

2013 ◽  
Vol 380-384 ◽  
pp. 3442-3445
Author(s):  
You Gang Zhang ◽  
Rui Li
Keyword(s):  
Cost Control ◽  
Singular Systems ◽  
Guaranteed Cost Control ◽  
Feasibility Problem ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Guaranteed Cost ◽  
Varying Time Delay ◽  
Interval Systems

The problem of resilient guaranteed cost control for a class of singular interval systems with time varying time-delay was investigated. A condition for the existence of resilient guaranteed cost controller is derived via linear matrix inequalities (LMI) technology. Furthermore, it is shown that this condition is equivalent to the feasibility problem of a set of LMIs, and its solutions provide a parameterized representation of resilient guaranteed cost controllers. Finally, a numerical example is given to show the effectiveness of it.

scholarly journals Finite-Time H ∞ State Estimation for Markovian Jump Neural Networks with Time-Varying Delays via an Extended Wirtinger’s Integral Inequality

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Saravanan Shanmugam ◽  
M. Syed Ali ◽  
R. Vadivel ◽  
Gyu M. Lee
Keyword(s):  
Neural Networks ◽  
Finite Time ◽  
Transition Probabilities ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Markovian Jump ◽  
Markovian Jumping ◽  
Double Inequality ◽  
Markovian Jump Neural Networks

This study investigates the finite-time boundedness for Markovian jump neural networks (MJNNs) with time-varying delays. An MJNN consists of a limited number of jumping modes wherein it can jump starting with one mode then onto the next by following a Markovian process with known transition probabilities. By constructing new Lyapunov–Krasovskii functional (LKF) candidates, extended Wirtinger’s, and Wirtinger’s double inequality with multiple integral terms and using activation function conditions, several sufficient conditions for Markovian jumping neural networks are derived. Furthermore, delay-dependent adequate conditions on guaranteeing the closed-loop system which are stochastically finite-time bounded (SFTB) with the prescribed H ∞ performance level are proposed. Linear matrix inequalities are utilized to obtain analysis results. The purpose is to obtain less conservative conditions on finite-time H ∞ performance for Markovian jump neural networks with time-varying delay. Eventually, simulation examples are provided to illustrate the validity of the addressed method.

Delay-dependent guaranteed cost control for a non-linear stochastic system with distributed delays

2009 ◽  
Vol 223 (6) ◽  
pp. 763-772 ◽  
Author(s):  
J Qiu ◽  
H He ◽  
P Shi
Keyword(s):  
Stochastic Systems ◽  
Cost Control ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Guaranteed Cost Control ◽  
Linear Matrix ◽  
Guaranteed Cost ◽  
Non Linear ◽  
Delay Dependent ◽  
Delay Dependent Stability

In this paper, the problem of guaranteed cost control for stochastic systems is considered. The system is non-linear, and the delays are distributed. Based on Lyapunov stability theory combined with the linear matrix inequality (LMI) technique, delay-dependent stability and stabilization conditions are proposed. Furthermore, sufficient conditions for the existence of guaranteed cost controllers are derived. Finally, a numerical example is used to illustrate the effectiveness and feasibility of the approaches proposed in this paper.

scholarly journals Finite-time stabilization of switched nonlinear singular systems with asynchronous switching

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jing Wang ◽  
Xingtao Wang
Keyword(s):  
Finite Time ◽  
Singular Systems ◽  
Singular System ◽  
Sufficient Conditions ◽  
Original System ◽  
Linear Matrix ◽  
Finite Time Stability ◽  
Nonlinear Singular Systems ◽  
Time Period ◽  
Finite Time Stabilization

AbstractThis paper is concerned with the finite-time stabilization of a class of switched nonlinear singular systems under asynchronous control. Asynchronism here refers to the delays in switching between the controller and the subsystem. First, the dynamic decomposition technique is used to prove that such a switched singular system is regular and impulse-free. Secondly, based on the state solutions of the closed-loop system in the matched time period and the mismatched time period of the system instead of constructing a Lyapunov function, the sufficient conditions for the finite-time stability of the asynchronous switched singular system are given, there is no limit to the stability of subsystems. Then, the mode-dependent state feedback controller that makes the original system stable is derived in the form of strict linear matrix inequalities. Finally, numerical examples are given to verify the feasibility and validity of the results.

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