A Robust $H_{\infty}$ Non-PDC Design Scheme for Singularly Perturbed T–S Fuzzy Systems With Immeasurable State Variables

2015 ◽  
Vol 23 (3) ◽  
pp. 525-541 ◽  
Author(s):  
Mohammad Hassan Asemani ◽  
Vahid Johari Majd
Keyword(s):  
Fuzzy Systems ◽  
Singularly Perturbed ◽  
State Variables ◽  
Design Scheme

Filter design for discrete-time singularly perturbed T–S fuzzy systems

2013 ◽  
Vol 350 (10) ◽  
pp. 3011-3028 ◽  
Author(s):  
Tong Peng ◽  
Chunsong Han ◽  
Yongyang Xiong ◽  
Ligang Wu ◽  
Baojun Pang
Keyword(s):  
Discrete Time ◽  
Fuzzy Systems ◽  
Filter Design ◽  
Singularly Perturbed

Control Synthesis of Singularly Perturbed Fuzzy Systems

2008 ◽  
Vol 16 (3) ◽  
pp. 615-629 ◽  
Author(s):  
Guang-Hong Yang ◽  
Jiuxiang Dong
Keyword(s):  
Fuzzy Systems ◽  
Singularly Perturbed ◽  
Control Synthesis

scholarly journals Recursive Reduced-Order Algorithm for Singularly Perturbed Cross Grammian Algebraic Sylvester Equation

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Intessar Al-Iedani ◽  
Zoran Gajic
Keyword(s):  
Recursive Algorithm ◽  
Perturbation Parameter ◽  
Singularly Perturbed ◽  
Sylvester Equation ◽  
State Variables ◽  
Reduced Order ◽  
Aggregate Information ◽  
The Cross ◽  
Perturbed Linear Systems ◽  
Controllability And Observability

A new recursive algorithm is developed for solving the algebraic Sylvester equation that defines the cross Grammian of singularly perturbed linear systems. The cross Grammian matrix provides aggregate information about controllability and observability of a linear system. The solution is obtained in terms of reduced-order algebraic Sylvester equations that correspond to slow and fast subsystems of a singularly perturbed system. The rate of convergence of the proposed algorithm isOε, whereεis a small singular perturbation parameter that indicates separation of slow and fast state variables. Several real physical system examples are solved to demonstrate efficiency of the proposed algorithm.

scholarly journals A Quasi-Steady State Model of a Singularly Perturbed Wind Turbine with an Induction Generator and Nonlinear Frictions: A Bond Graph Approach

2020 ◽  
Vol 2020 ◽  
pp. 1-26
Author(s):  
Aaron Padilla-Garcia ◽  
Gilberto Gonzalez-Avalos ◽  
Noe Barrera-Gallegos ◽  
Gerardo Ayala-Jaimes
Keyword(s):  
Steady State ◽  
Nonlinear Systems ◽  
Wind Turbine ◽  
Bond Graph ◽  
Singularly Perturbed ◽  
State Model ◽  
Induction Generator ◽  
Quasi Steady State ◽  
State Variables ◽  
Steady State Model

The modelling in bond graph of a class of nonlinear systems with singular perturbations is presented. The class of nonlinear systems modelled by bond graphs is defined by the product of state variables and nonlinear dissipation elements. In order to obtain the mathematical model of the singularly perturbed nonlinear systems, a lemma based on the junction structure of the bond graph with a preferred integral causality assignment is proposed. The quasi-steady state model of the system is obtained by assigning a derivative causality to the storage elements for the fast dynamics and an integral causality to the storage elements for the slow dynamics. The proposed methodology to a wind turbine connected to an induction generator is applied. Simulation results of the exact and reduced models of this case study are shown.

scholarly journals Direct Determination of Reduced Models of a Class of Singularly Perturbed Nonlinear Systems on Three Time Scales in a Bond Graph Approach

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 104
Author(s):  
Gerardo Ayala-Jaimes ◽  
Gilberto Gonzalez-Avalos ◽  
Noe Barrera Gallegos ◽  
Aaron Padilla Garcia ◽  
Juancarlos Mendez-B
Keyword(s):  
Nonlinear Systems ◽  
Dynamic Model ◽  
Time Scales ◽  
Bond Graph ◽  
Singularly Perturbed ◽  
Fast Time ◽  
State Variables ◽  
Slow Dynamics ◽  
Reduced Models ◽  
Bond Graph Modeling

One of the most important features in the analysis of the singular perturbation methods is the reduction of models. Likewise, the bond graph methodology in dynamic system modeling has been widely used. In this paper, the bond graph modeling of nonlinear systems with singular perturbations is presented. The class of nonlinear systems is the product of state variables on three time scales (fast, medium, and slow). Through this paper, the symmetry of mathematical modeling and graphical modeling can be established. A main characteristic of the bond graph is the application of causality to its elements. When an integral causality is assigned to the storage elements that determine the state variables, the dynamic model is obtained. If the storage elements of the fast dynamics have a derivative causality and the storage elements of the medium and slow dynamics an integral causality is assigned, a reduced model is obtained, which consists of a dynamic model for the medium and slow time scales and a stationary model of the fast time scale. By applying derivative causality to the storage elements of the fast and medium dynamics and an integral causality to the storage elements of the slow dynamics, the quasi-steady-state model for the slow dynamics is obtained and stationary models for the fast and medium dynamics are defined. The exact and reduced models of singularly perturbed systems can be interpreted as another symmetry in the development of this paper. Finally, the proposed methodology was applied to a system with three time scales in a bond graph approach, and simulation results are shown in order to indicate the effectiveness of the proposed methodology.

scholarly journals Dynamic Output-Feedback Passivity Control for Fuzzy Systems under Variable Sampling

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Hongyi Li ◽  
Xingjian Sun ◽  
H. R. Karimi ◽  
Ben Niu
Keyword(s):  
Output Feedback ◽  
Fuzzy Systems ◽  
Output Feedback Control ◽  
Optimization Approach ◽  
Dynamic Output Feedback ◽  
State Variables ◽  
Sampled Data ◽  
Control Approach ◽  
Dynamic Output ◽  
Variable Sampling

This paper concerns the problem of dynamic output-feedback control for a class of nonlinear systems with nonuniform uncertain sampling via Takagi-Sugeno (T-S) fuzzy control approach. The sampling is not required to be periodic, and the state variables are not required to be measurable. A new type fuzzy dynamic output-feedback sampled-data controller is constructed, and a novel time-dependent Lyapunov-Krasovskii functional is chosen for fuzzy systems under variable sampling. By using Lyapunov stability theory, a sufficient condition for very-strict passive analysis of fuzzy systems with nonuniform uncertain sampling is derived. Based on this condition, a novel fuzzy dynamic output-feedback controller is designed such that the closed-loop system is very-strictly passive. The existence condition of the controller can be solved by convex optimization approach. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.

Dissipative Control for Singularly Perturbed Fuzzy Systems

2008 ◽  
Vol 41 (2) ◽  
pp. 14444-14448
Author(s):  
Ji-Chang Lo ◽  
Shang-Yi Gau
Keyword(s):  
Fuzzy Systems ◽  
Singularly Perturbed ◽  
Dissipative Control

Stabilization of Singularly Perturbed Fuzzy Systems

2004 ◽  
Vol 12 (5) ◽  
pp. 579-595 ◽  
Author(s):  
T.-H.S. Li ◽  
K.-J. Lin
Keyword(s):  
Fuzzy Systems ◽  
Singularly Perturbed
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