The Optimal Regulations of the Interconnection-Degrees of Large Scale Systems under Instable Case

2012 ◽  
Vol 235 ◽  
pp. 107-110
Author(s):  
Ying Ge Wo
Keyword(s):  
Cost Function ◽  
Linear Matrix Inequalities ◽  
Large Scale ◽  
Large System ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequalities ◽  
Stabilization Problem ◽  
Large Scale Systems ◽  
The Cost

This paper discusses the stabilization problem of a large-scale system via cutting off the connections or decreasing the degree of interconnections among its subsystems subject to a cost function. Under the assumption that the large system is unstable but its sub-systems are all stable, a sufficient condition about the degree of interconnection is presented via cutting off the connections or decreasing the degree of interconnections among its subsystems such that the new large system is stable. This condition can be expressed by linear matrix inequalities (LMIs). Based on this analysis, an optimal regulation for such controls is obtained ensures the minimization of the cost function. An illustrating example is also given to show the effectiveness of the proposed method.

Non-Fragile Decentralized Control for the Uncertain Singular Large-Scale Systems with Time-Delay

2011 ◽  
Vol 317-319 ◽  
pp. 2204-2207
Author(s):  
Dong Mei Yang ◽  
Qing Sun
Keyword(s):  
Time Delay ◽  
Linear Matrix Inequalities ◽  
Decentralized Control ◽  
Large Scale ◽  
Controller Design ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequalities ◽  
Large Scale Systems ◽  
System With Time Delay

This paper is concerned with the non-fragile decentralized controller design problem for uncertain singular large-scale system with time-delay. Sufficient condition for the controller is expressed in terms of linear matrix inequalities(LMIs). When this condition is feasible, the desired controller can be obtained with additive gain perturbations and multiplicative gain perturbations. Finally, a numerical example is also given to illustrate the effectiveness.

scholarly journals Robust and NonfragileH∞Kalman-Type Filter Design for Parameter-Uncertain Time-Delay Systems: PLMI Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Seung Hyeop Yang ◽  
Hong Bae Park
Keyword(s):  
Time Delay ◽  
Linear Matrix Inequalities ◽  
Filter Design ◽  
Estimation Error ◽  
Delay Systems ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Time Delay Systems ◽  
Matrix Inequalities ◽  
Parameter Uncertainties

This paper describes the synthesis of a robust and nonfragileH∞Kalman-type filter design for a class of time-delay systems with polytopic uncertainties, filter-gain variations, and disturbances. We present the sufficient condition for filter existence and the method for designing a robust nonfragileH∞filter by using LMIs (Linear Matrix Inequalities) technique. Because the obtained sufficient condition can be represented as PLMIs (Parameterized Linear Matrix Inequalities), which can generate infinite LMIs, we use a relaxation technique to find finite solutions for a robust nonfragileH∞filter. We show that the proposed filter can minimize estimation error in terms of parameter uncertainties, filter-fragility, and disturbances.

scholarly journals Synthesis of Decentralized Variable Gain Robust Controllers with GuaranteedL2Gain Performance for a Class of Uncertain Large-Scale Interconnected Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Shunya Nagai ◽  
Hidetoshi Oya
Keyword(s):  
Linear Matrix Inequalities ◽  
Large Scale ◽  
Sufficient Conditions ◽  
Matching Condition ◽  
Interconnected Systems ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Robust Controller ◽  
Interconnected System ◽  
Variable Gain

We consider a design problem of a decentralized variable gain robust controller with guaranteedL2gain performance for a class of uncertain large-scale interconnected systems. For the uncertain large-scale interconnected system, the uncertainties and the interactions satisfy the matching condition. In this paper, we show that sufficient conditions for the existence of the proposed decentralized variable gain robust controller with guaranteedL2gain performance are given in terms of linear matrix inequalities (LMIs). Finally, simple illustrative examples are shown.

scholarly journals On the stability of 2D general Roesser Lyapunov systems

Mathematica ◽  
2021 ◽  
Vol 63 (86) (1) ◽  
pp. 85-97
Author(s):  
Mohammed Amine Ghezzar ◽  
Djillali Bouagada ◽  
Kamel Benyettou ◽  
Mohammed Chadli ◽  
Paul Van Dooren
Keyword(s):  
Asymptotic Stability ◽  
Linear Matrix Inequalities ◽  
Discrete Time ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Two Dimensional ◽  
Matrix Inequalities ◽  
The Stability

This paper addresses the problem of stability for general two-dimensional (2D) discrete-time and continuous-discrete time Lyapunov systems, where the linear matrix inequalities (LMI's) approach is applied to derive a new sufficient condition for the asymptotic stability.

Robust and Non-Fragile H∞ Observer-Based Filter Design for Parameter Uncertain System Using PLMI Approach

2013 ◽  
Vol 373-375 ◽  
pp. 685-688
Author(s):  
Seung Hyeop Yang ◽  
Seung Hyun Paik ◽  
Hong Bae Park
Keyword(s):  
Linear Matrix Inequalities ◽  
Filter Design ◽  
Estimation Error ◽  
Uncertain System ◽  
Relaxation Technique ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
Polytopic Uncertainties

This paper describes the synthesis of a robust and non-fragile H∞ observer-based filter design for a class of parameter uncertain system with polytopic uncertainties, disturbances, and gain variations. We present the sufficient condition for filter existence and the method for designing a robust and non-fragile H∞ filter by using LMIs (Linear Matrix Inequalities) technique. Because the obtained sufficient condition can be represented as PLMIs (Parameterized Linear Matrix Inequalities), which can generate infinite LMIs, we use the relaxation technique to find finite solutions for a robust and non-fragile H∞ filter. We show that the proposed filter can minimize the estimation error in terms of parameter uncertainties, filter-fragility, and disturbances.

Robust H∞ Control for Takagi-Sugeno Fuzzy Systems with Time-Varying Delays in State and Input

2015 ◽  
Vol 764-765 ◽  
pp. 624-628 ◽  
Author(s):  
Shun Hung Tsai ◽  
Siou An Jian
Keyword(s):  
Time Delay ◽  
Linear Matrix Inequalities ◽  
Fuzzy Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Stabilization Problem ◽  
State And Input Delays ◽  
Input Delays ◽  
Takagi Sugeno

In this paper, the robust H∞ stabilization problem for Takagi-Sugeno fuzzy control systemswith state and input delays is explored. Based on a Lyapunov-Krasoviskii function, the delaydependentstabilization conditions are proposed in terms of linear matrix inequalities (LMIs) to guaranteethe asymptotic stabilization of time-delay Takagi-Sugeno fuzzy systems with disturbance input.Finally, a numerical example is illustrated to demonstrate the feasibility and effectiveness of the proposed stabilization.

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