scholarly journals H∞Control of Pairwise Distributable Large-Scale TS Fuzzy Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-18
Author(s):  
Anna Filasová ◽  
Dušan Krokavec
Keyword(s):  
Fuzzy Systems ◽  
Large Scale ◽  
Tuning Parameter ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Bounded Real Lemma ◽  
Control Scheme ◽  
State Controller ◽  
Lyapunov Matrix ◽  
Takagi Sugeno

The paper presents new conditions suitable in design of the stabilizing state controller for a class of continuous-time nonlinear systems, which are representable by pairwise distributable Takagi-Sugeno models. Taking into account the affine properties of the TS model structure and applying the pairwise subsystems fuzzy control scheme relating to the parallel distributed output compensators, the extended bounded real lemma form and the sufficient design conditions for pairwise decentralized control are outlined in terms of linear matrix inequalities. The proposed procedure decouples the Lyapunov matrix and the system parameter matrices in the LMIs and, using free tuning parameter, provides the way to obtain global stability of such large-scale TS systems and optimizes subsystems interactionH∞norm bounds.

scholarly journals Stabilizing Fuzzy Output Control for a Class of Nonlinear Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Dušan Krokavec ◽  
Anna Filasová
Keyword(s):  
Nonlinear Systems ◽  
Design Method ◽  
Design Procedure ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Output Control ◽  
Output Controller ◽  
Control Scheme ◽  
Lyapunov Matrix ◽  
Takagi Sugeno

The paper presents new conditions suitable in design of a stabilizing output controller for a class of continuous-time nonlinear systems, represented by Takagi-Sugeno models. Taking into account the affine properties of the TS model structure and applying the fuzzy control scheme relating to the parallel distributed output compensators, the sufficient design conditions are outlined in terms of linear matrix inequalities. The proposed procedure decouples the Lyapunov matrix and the system parameter matrices in the LMIs and guarantees global stability of the system. Simulation result illustrates the design procedure and demonstrates the performances of the proposed design method.

scholarly journals Finite frequency model reduction for 2-D fuzzy systems in FM model

2021 ◽  
Vol 297 ◽  
pp. 01035
Author(s):  
Rachid Naoual ◽  
Abderrahim El-Amrani ◽  
Ismail Boumhidi
Keyword(s):  
Model Reduction ◽  
State Space ◽  
Linear Matrix Inequalities ◽  
Fuzzy Systems ◽  
Linear Matrix ◽  
Two Dimensional ◽  
Matrix Inequalities ◽  
Finite Frequency ◽  
Frequency Model ◽  
Takagi Sugeno

This paper deals with the problem of H∞ model reduction for two-dimensional (2D) discrete Takagi-Sugeno (T-S) fuzzy systems described by Fornasini-Marchesini local state-space (FM LSS) models, over finite frequency (FF) domain. New design conditions guaranteeing the FF H∞ model reduction are established in terms of Linear Matrix Inequalities (LMIs). To highlight the effectiveness of the proposed H∞ model reduction design, a numerical example is given.

Constrained stochastic control of positive Takagi-Sugeno fuzzy systems with Markov jumps and its application to a DC-DC boost converter

2020 ◽  
Vol 42 (16) ◽  
pp. 3234-3242
Author(s):  
Mohamed Aatabe ◽  
Fatima El Guezar ◽  
Hassane Bouzahir ◽  
Alessandro N Vargas
Keyword(s):  
Fuzzy Systems ◽  
Boost Converter ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Markov Jump ◽  
Load Variations ◽  
Stabilization Control ◽  
Mean Square Stability ◽  
Time Formulation ◽  
Takagi Sugeno

This paper presents a stabilization control for positive, Takagi-Sugeno fuzzy systems subject to Markov jump parameters. In the continuous-time formulation, the approach guarantees mean-square stability with constraints on the control—the main condition hinges upon linear matrix inequalities. The proposed method’s usefulness is illustrated by a practical-oriented example, which was designed to control the output voltage of a DC-DC boost converter subject to both voltage and load variations driven by a Markov chain.

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.

Finite-Frequency Static Output Feedback H∞ Control of Continuous-Time T–S Fuzzy Systems

2018 ◽  
Vol 28 (02) ◽  
pp. 1950023 ◽  
Author(s):  
Redouane Chaibi ◽  
Ismail Er Rachid ◽  
El Houssaine Tissir ◽  
Abdelaziz Hmamed
Keyword(s):  
Output Feedback ◽  
Continuous Time ◽  
Fuzzy Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Static Output Feedback ◽  
Matrix Inequalities ◽  
Finite Frequency ◽  
Takagi Sugeno ◽  
Static Output

This paper is concerned with finite-frequency static output feedback (SOF) [Formula: see text] control for a class of continuous-time Takagi–Sugeno (T–S) fuzzy systems. With the aid of the generalized Kalman–Yakubovich–Popov (GKYP) lemma, sufficient conditions for the existence of the finite-frequency SOF [Formula: see text] control are presented. The bilinear matrix inequalities are converted to a set of linear matrix inequalities, with the aid of some special derivations. Two practical examples are given to demonstrate the effectiveness of the proposed method.

Generalized non-monotonic Lyapunov functions for analysis and synthesis of Takagi-Sugeno fuzzy systems

2020 ◽  
Vol 39 (3) ◽  
pp. 4147-4158
Author(s):  
Pedro H.S. Coutinho ◽  
Márcia L.C. Peixoto ◽  
Márcio J. Lacerda ◽  
Miguel Bernal ◽  
Reinaldo M. Palhares
Keyword(s):  
Lyapunov Functions ◽  
Fuzzy Systems ◽  
State Of The Art ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Current State ◽  
Quadratic Lyapunov Functions ◽  
Analysis And Synthesis ◽  
Takagi Sugeno

This paper presents new stability and stabilisation conditions in the form of linear matrix inequalities for discrete-time Takagi-Sugeno fuzzy systems; they are derived considering a class of non-quadratic Lyapunov functions with multi-parametric non-monotonic terms, which significantly enhances the feasibility set of current state-of-the-art results. In addition, extensions to cope with the disturbance attenuation control problem are included. Benchmark numerical examples are provided to illustrate the effectiveness of the proposed approach.

scholarly journals FTC with Dynamic Virtual Actuators: Characterization via Dynamic Output Controllers andH∞Approach

2015 ◽  
Vol 2015 ◽  
pp. 1-16 ◽  
Author(s):  
Dušan Krokavec ◽  
Anna Filasová ◽  
Vladimír Serbák
Keyword(s):  
Fault Tolerant ◽  
Tuning Parameter ◽  
Linear Matrix ◽  
Closed Loop System ◽  
Control Structures ◽  
Output Controller ◽  
Bounded Real Lemma ◽  
Dynamic Output ◽  
Control Scheme ◽  
Time Linear

The paper presents new conditions, adequate in design of dynamic virtual actuators and utilizable in fault-tolerant control structures (FTC) for continuous-time linear systems, which are stabilizable by dynamic output controllers. Taking into account disturbance conditions and changes of variables in FTC after virtual actuator activation and applying the nominal control scheme relating to the biproper dynamic output controller of prescribed order, the design conditions are outlined in terms of the linear matrix inequalities within the enhanced bounded real lemma forms. Using a free tuning parameter in design, and with suitable choice of the controller order, the approach provides the way to obtain acceptable dynamics of the closed-loop system after activation of the dynamic virtual actuator.

Stability of a Class of Discrete-Time Switched Fuzzy Systems by Arbitrary Switching

2014 ◽  
Vol 536-537 ◽  
pp. 1187-1190
Author(s):  
Hong Yang ◽  
Huan Huan Lü ◽  
Le Zhang
Keyword(s):  
Discrete Time ◽  
Fuzzy System ◽  
Lyapunov Functions ◽  
Fuzzy Systems ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Simulation Experiments ◽  
Arbitrary Switching ◽  
Lyapunov Functions Method ◽  
Takagi Sugeno

This paper investigates a representation model, namely, a discrete-time switched fuzzy system. In this model, a system is a switched system whose subsystems are all discrete-time Takagi-Sugeno (T-S) fuzzy systems. For the proposed discrete-time switched fuzzy system is built to ensure that the relevant system is asymptotically stable by Arbitrary Switching and the Lyapunov functions method. The main conditions are given in form of linear matrix inequalities (LMIs), which are easily solvable. The elaborated illustrative examples and the respective simulation experiments demonstrate the effectiveness of the proposed method.

Robust Tracking Control for Takagi–Sugeno Fuzzy Systems With Unmeasurable Premise Variables: Application to Tank System

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
H. Ghorbel ◽  
A. El Hajjaji ◽  
M. Souissi ◽  
M. Chaabane
Keyword(s):  
Tracking Control ◽  
Fuzzy Systems ◽  
Design Procedure ◽  
Control Design ◽  
Linear Matrix ◽  
Robust Tracking Control ◽  
Fuzzy Observer ◽  
Tank System ◽  
System States ◽  
Takagi Sugeno

In this paper, a robust fuzzy observer-based tracking controller for continuous-time nonlinear systems presented by Takagi–Sugeno (TS) models with unmeasurable premise variables, is synthesized. Using the H∞ norm and Lyapunov approach, the control design for TS fuzzy systems with both unmeasurable premises and system states is developed to guarantee tracking performance of closed loop systems. Sufficient relaxed conditions for synthesis of the fuzzy observer and the fuzzy control are driven in terms of linear matrix inequalities (LMIs) constraints. The proposed method allows simplifying the design procedure and gives the observer and controller gains in only one step. Numerical simulation on a two tank system is provided to illustrate the tracking control design procedure and to confirm the efficiency of the proposed method.

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