scholarly journals H∞Observers Design for a Class of Continuous Time Nonlinear Singular Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Mohamed Zerrougui ◽  
Latifa Boutat-Baddas ◽  
Mohamed Darouach
Keyword(s):  
Singular Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Minimal Order ◽  
Estimation Errors ◽  
Worst Case ◽  
Reduced Order ◽  
Lipschitz Continuous ◽  
Nonlinear Singular Systems ◽  
Error Energy

This paper considers the problem ofH∞observers design for a class of Lipschitz continuous nonlinear singular systems. The method is based on the parameterization of the solution of the generalized Sylvester equations obtained from the estimation errors. Sufficient conditions for the existence of the observers which guarantee stability and the worst case observers error energy over all bounded energy disturbances is minimized are given. The approach also unifies the full-order, the reduced-order, and the minimal-order observers design. The solutions are obtained through linear matrix inequalities (LMIs) formulation. A numerical example is given to illustrate our results.

scholarly journals H∞ Filtering for Discrete-Time Nonlinear Singular Systems with Quantization

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Yifu Feng ◽  
Zhi-Min Li ◽  
Xiao-Heng Chang
Keyword(s):  
Discrete Time ◽  
Filter Design ◽  
Design Method ◽  
Singular Systems ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Nonlinear Singular Systems ◽  
Attenuation Level ◽  
Measurement Output

This paper investigates the problem of H∞ filtering for class discrete-time Lipschitz nonlinear singular systems with measurement quantization. Assume that the system measurement output is quantized by a static, memoryless, and logarithmic quantizer before it is transmitted to the filter, while the quantizer errors can be treated as sector-bound uncertainties. The attention of this paper is focused on the design of a nonlinear quantized H∞ filter to mitigate quantization effects and ensure that the filtering error system is admissible (asymptotically stable, regular, and causal), while having a unique solution with a prescribed H∞ noise attenuation level. By introducing some slack variables and using the Lyapunov stability theory, some sufficient conditions for the existence of the nonlinear quantized H∞ filter are expressed in terms of linear matrix inequalities (LMIs). Finally, a numerical example is presented to demonstrate the effectiveness of the proposed quantized filter design method.

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.

Robust H2 Output Feedback Controller Design for Damping Power System Oscillations

2017 ◽  
Vol 6 (10) ◽  
pp. 8
Author(s):  
Kho Hie Kwee ◽  
Hardiansyah .
Keyword(s):  
Power System ◽  
Output Feedback ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Feedback Controller ◽  
Linear Matrix ◽  
Parameter Uncertainties ◽  
Worst Case ◽  
Output Feedback Controller ◽  
Power System Oscillations

This paper addresses the design problem of robust H2 output feedback controller design for damping power system oscillations. Sufficient conditions for the existence of output feedback controllers with norm-bounded parameter uncertainties are given in terms of linear matrix inequalities (LMIs). Furthermore, a convex optimization problem with LMI constraints is formulated to design the output feedback controller which minimizes an upper bound on the worst-case H2 norm for a range of admissible plant perturbations. The technique is illustrated with applications to the design of stabilizer for a single-machine infinite-bus (SMIB) power system. The LMI based control ensures adequate damping for widely varying system operating.

scholarly journals Stability and Stabilization of Continuous-Time Markovian Jump Singular Systems with Partly Known Transition Probabilities

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Jumei Wei ◽  
Rui Ma
Keyword(s):  
Continuous Time ◽  
Controller Design ◽  
Partial Information ◽  
Transition Probabilities ◽  
Singular Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Markovian Jump ◽  
Stability And Stabilization ◽  
The Stability

This paper investigates the problem of the stability and stabilization of continuous-time Markovian jump singular systems with partial information on transition probabilities. A new stability criterion which is necessary and sufficient is obtained for these systems. Furthermore, sufficient conditions for the state feedback controller design are derived in terms of linear matrix inequalities. Finally, numerical examples are given to illustrate the effectiveness of the proposed methods.

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 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.

Robust Stabilization of Stochastic Singular Systems with Markovian Switching

2012 ◽  
Vol 591-593 ◽  
pp. 1496-1501
Author(s):  
Yu Cai Ding ◽  
Hong Zhu ◽  
Yu Ping Zhang ◽  
Yong Zeng
Keyword(s):  
Robust Stability ◽  
Singular Systems ◽  
Robust Stabilization ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Parameter Uncertainties ◽  
Markovian Jump Parameters ◽  
Stochastic Disturbance ◽  
Stability And Stabilization ◽  
Robust Stability And Stabilization

In this paper, robust stability and stabilization of singular stochastic hybrid systems are investigated. The system under consideration involves parameter uncertainties, Itô-type stochastic disturbance, Markovian jump parameters as well as time-varying delays. The aim of this paper is to design a state controller such that the dynamic system is robust stable. By using the Lyapunov-Krasovskii functional and Itô's differential rule, delay-range-dependent sufficient conditions on robust stability and stabilization are obtained in the form of linear matrix inequalities (LMIs). A numerical example is given to illustrate the effectiveness of the proposed main results.

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.

Convex Stability Analysis of Nonlinear Singular Systems via Linear Matrix Inequalities

2019 ◽  
Vol 64 (4) ◽  
pp. 1740-1745 ◽  
Author(s):  
Juan Carlos Arceo ◽  
Marcelino Sanchez ◽  
Victor Estrada-Manzo ◽  
Miguel Bernal
Keyword(s):  
Stability Analysis ◽  
Linear Matrix Inequalities ◽  
Singular Systems ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Nonlinear Singular Systems

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.

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