scholarly journals Passive Control of Switched Singular Systems via Output Feedback

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Shuhui Shi ◽  
Guoliang Wang ◽  
Jianhua Wang ◽  
Hong Li
Keyword(s):  
Output Feedback ◽  
Passive Control ◽  
Singular Systems ◽  
Singular System ◽  
Inverse Matrix ◽  
Linear Matrix ◽  
Controller Gain ◽  
Nonlinear Inequality ◽  
Matrix Variable ◽  
Lyapunov Matrix

An instrumental matrix approach to design output feedback passive controller for switched singular systems is proposed in this paper. The nonlinear inequality condition including Lyapunov inverse matrix and controller gain matrix is decoupled by introducing additional instrumental matrix variable. Combined with multiple Lyapunov function method, the nonlinear inequality is transformed into linear matrix inequality (LMI). An LMI condition is presented for switched singular system to be stable and passive via static output feedback under designed switching signal. Moreover, the conditions proposed do not require the decomposition of Lyapunov matrix and its inverse matrix or fixing to a special structure. The theoretical results are verified by means of an example. The method introduced in the paper can be effectively extended to a single singular system and normal switched system.

scholarly journals H∞ Reliable Dynamic Output-Feedback Controller Design for Discrete-Time Singular Systems with Sensor Saturation

Actuators ◽  
2021 ◽  
Vol 10 (8) ◽  
pp. 196
Author(s):  
Mourad Kchaou ◽  
Houssem Jerbi ◽  
Naim Ben Ali ◽  
Haitham Alsaif
Keyword(s):  
Discrete Time ◽  
Output Feedback ◽  
Fault Tolerant ◽  
Singular Systems ◽  
Singular System ◽  
System Stability ◽  
Linear Matrix ◽  
Dynamic Output Feedback ◽  
Dynamic Output ◽  
Sensor Saturation

In this study, we investigate the H∞ fault-tolerant control problem for a discrete-time singular system which is subject to external disturbances, actuator faults, and sensor saturation. By assuming that the state variable of the system is unavailable for measurement, and the actuator fault can be described by a Markovian jump process, attention is mainly focused on designing a reliable dynamic output-feedback (DOF) controller able to compensate for the effects of the aforementioned factors on the system stability and performance. Based on the sector non-linear approach to handle the sensor saturation, a new criterion is established to ensure that the closed-loop system is stochastically admissible with a γ level of the H∞ disturbance rejection performance. The main aim of this work is to develop a procedure for synthesizing the controller gains without any model transformation or decomposition of the output matrix. Therefore, by introducing a slack variable, the H∞ admissibility criterion is successfully transformed in terms of strict linear matrix inequalities (LMIs). Three practical examples are exploited to test the feasibility and effectiveness of the proposed approach.

Delay-Dependent Robust Passive Control for Uncertain Discrete Singular Systems with Multiple Time-Delays

2012 ◽  
Vol 433-440 ◽  
pp. 4284-4290
Author(s):  
Shu Hong Tang ◽  
Bo Meng ◽  
Cun Chen Gao
Keyword(s):  
Time Delays ◽  
Passive Control ◽  
Singular Systems ◽  
Singular System ◽  
Linear Matrix ◽  
Multiple Time ◽  
Weighting Matrix ◽  
Multiple Time Delays ◽  
Discrete Singular Systems ◽  
Delay Dependent

This paper investigates delay-dependent robust passive analysis and control for uncertain discrete singular system with multiple time-delays. Delay-dependent robust passive sufficient condition in terms of linear matrix inequalities (LMI) for the discrete singular systems is obtained by employing Lyapunov-Krasovskii approach and free weighting matrix technique. Based on this condition, a delay-dependent robust passive controller is presented which guarantees the resultant closed-loop system to be regular, casual, stable and robust passive. A numerical example is provided to demonstrate the effectiveness of the method.

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.

Regional Pole Placement via Static Output Feedback Based on Coordinate Transformation

2012 ◽  
Vol 546-547 ◽  
pp. 916-921
Author(s):  
Hai Bin Shi ◽  
Li Qi
Keyword(s):  
Output Feedback ◽  
Coordinate Transformation ◽  
Pole Placement ◽  
Linear Matrix ◽  
Feedback Gain ◽  
Static Output Feedback ◽  
Gain Matrix ◽  
Matrix Variable ◽  
Regional Pole Placement ◽  
Static Output

This paper focuses on the regional pole placement via static output feedback. Under proper state coordinate transformation with a free matrix variable, the static output feedback gain may be obtained by solving a linear matrix inequality (LMI). The LMI is feasible only if the poles of a dummy control system are in the given LMI region. The free matrix variable can regulate the dummy system as a state feedback gain matrix. So once the free variable is determined, the static output feedback gain matrix may be obtained by an LMI-based method. The main computations do not concern any reduction or enlargement of matrix inequalities. Numerical examples show the effectiveness of the proposed algorithm.

scholarly journals Robust Fault Estimation for a Class of T-S Fuzzy Singular Systems with Time-Varying Delay via Improved Delay Partitioning Approach

2016 ◽  
Vol 2016 ◽  
pp. 1-15 ◽  
Author(s):  
Chao Sun ◽  
FuLi Wang ◽  
XiQin He
Keyword(s):  
Singular Systems ◽  
Singular System ◽  
Fault Estimation ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
System A ◽  
Delay Dependent ◽  
Takagi Sugeno ◽  
Varying Delay

The problem of delay-dependent robust fault estimation for a class of Takagi-Sugeno (T-S) fuzzy singular systems is investigated. By decomposing the delay interval into two unequal subintervals and with a new and tighter integral inequality transformation, an improved delay-dependent stability criterion is given in terms of linear matrix inequalities (LMIs) to guarantee that the fuzzy singular system with time-varying delay is regular, impulse-free, and stable firstly. Then, based on this criterion, by considering the system fault as an auxiliary disturbance vector and constructing an appropriate fuzzy augmented system, a fault estimation observer is designed to ensure that the error dynamic system is regular, impulse-free, and robustly stable with a prescribedH∞performance satisfied for all actuator and sensor faults simultaneously, and the obtained fault estimates can practically better depict the size and shape of the faults. Finally, numerical examples are given to show the effectiveness of the proposed approach.

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 Robust Preview Control for Uncertain Discrete Singular Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Jiang Wu ◽  
Fucheng Liao ◽  
Yifan Shao ◽  
Shujie Gao ◽  
Hao Wang ◽  
...  
Keyword(s):  
Singular Systems ◽  
Singular System ◽  
Reference Signal ◽  
Linear Matrix ◽  
Preview Control ◽  
Forward Difference ◽  
Input Control ◽  
Discrete Singular Systems ◽  
Error System ◽  
The Stability

In this paper, the problem of robust preview control for uncertain discrete singular systems is considered. First of all, by employing the forward difference for uncertain discrete singular systems, the singular augmented error system with the state vector, the input control vector, and the previewable reference signal is derived. Since there is a singular matrix in the system, the existing method cannot be directly applied to this problem. By considering the stability of the transposition system with Linear Matrix Inequality (LMI) method, a new stability criterion for the transposition system is introduced. Then, the robust controller for the augmented error system is obtained, which is regarded as the robust preview controller for the original singular system. At last, the numerical simulation shows the correctness and effectiveness of the results.

Improved Results on Stability Criteria for Singular Systems with Interval Time-Varying Delays

2020 ◽  
pp. 2130001
Author(s):  
Chaibi Noreddine ◽  
Belamfedel Alaoui Sadek ◽  
Tissir El Houssaine ◽  
Bensalem Boukili
Keyword(s):  
Singular Systems ◽  
Singular System ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Small Gain ◽  
The Stability ◽  
Varying Delay ◽  
Singular Time

The purpose of this paper is to address the problem of assessing the stability of singular time-varying delay systems. In order to highlight the relations between the delay and the state, the singular system is transformed into a neutral form. Then, a model transformation using a three-terms approximation of the delayed state is exploited. Based on the lifting method and the Lyapunov–Krasovskii functional (LKF) method, a new linear matrix inequality (LMI) is obtained, allowing conclusions on stability to be drawn using the scaled small gain theorem (SSG). The use of SSG theorem for stability of singular systems with time-varying delay has not been investigated elsewhere in the literature. This represents the main novelty of this article. The result is applicable for assessing the stability of both singular systems and neutral systems with time-varying delays. The less conservativeness of the stability test is illustrated by comparison with recent literature 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.

Passive output feedback control for non-linear systems with time delays

2009 ◽  
Vol 223 (6) ◽  
pp. 737-743 ◽  
Author(s):  
X Luan ◽  
F Liu ◽  
P Shi
Keyword(s):  
Feedback Control ◽  
Linear Systems ◽  
Output Feedback ◽  
Time Delays ◽  
Passive Control ◽  
Output Feedback Control ◽  
Design Tool ◽  
Linear Matrix ◽  
Non Linear ◽  
Non Linear Systems

This paper focuses on the passive output feedback control problem for a class of non-linear systems with time delays. By using multilayer neural networks as an off-line-aided design tool, a dynamic output feedback controller with certain dissipation is developed using the passive control theory in terms of linear matrix inequalities (LMIs), which guarantees the closed-loop system asymptotically stable and strictly passive. It is shown that the solvability of the passive controller design problem is implied by the feasibility of LMIs. A numerical example is given to demonstrate the validity of the proposed approach.

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