scholarly journals On the nonlinear output regulation for systems described by Takagi-Sugeno fuzzy descriptor models with a steady-state mapping as an LMI optimization problem

2022 ◽  
Vol 9 (18) ◽  
pp. 85-91
Author(s):  
Luis A. Poblete ◽  
Tonatiuh Hernández-Cortés ◽  
Víctor Estrada-Manzo
Keyword(s):  
Steady State ◽  
Output Regulation ◽  
Descriptor Systems ◽  
Linear Matrix ◽  
Control Law ◽  
Lmi Optimization ◽  
Nonlinear Output Regulation ◽  
Fuzzy Descriptor Models ◽  
Takagi Sugeno ◽  
Output Regulation Problem

This paper is devoted to provide a numerical solution the nonlinear output regulation problem for descriptor systems. The control law under design is a nonlinear one, it consists on a nonlinear stabilizer combined with linear steady-state mapping as well as nonlinear steady-state input mapping; all of them are computed via linear matrix inequalities. A numerical example as well as a mechanical system as well are used to illustrate the viability of the proposed approach.

Admissible Conditions for T-S Fuzzy Descriptor Systems with Non-Differentiable Membership Functions

2013 ◽  
Vol 415 ◽  
pp. 259-266
Author(s):  
Peng Lin ◽  
Gang Hu
Keyword(s):  
Continuous Time ◽  
Lyapunov Functions ◽  
Closed Loop ◽  
Structural Information ◽  
Descriptor Systems ◽  
Linear Matrix ◽  
Membership Functions ◽  
Matrix Inequalities ◽  
Closed Loop Systems ◽  
Takagi Sugeno

In this paper, the admissible conditions (regular, impulse-free and stable) for a class of continuous-time Takagi-Sugeno (T-S) fuzzy descriptor systems are investigated. Sufficient admissible conditions for the closed-loop systems under non-parallel distributed compensation (non-PDC) feedback are proposed. This approach is mainly based on the state space division properly to make the membership functions continuous differentiable. Moreover, in order to make good use of the systems’ structural information in rules, the provided conditions are obtained through fuzzy Lyapunov functions candidate and can be formulated in terms of dilated Linear Matrix Inequalities (LMIs). Finally, the effectiveness of the proposed approach is shown through numerical example by using the optimization toolbox.

scholarly journals Takagi–Sugeno Fuzzy Control for a Nonlinear Networked System Exposed to a Replay Attack

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Reda El Abbadi ◽  
Hicham Jamouli
Keyword(s):  
Closed Loop ◽  
Inverted Pendulum ◽  
Networked Control System ◽  
Linear Matrix ◽  
Control Law ◽  
Closed Loop System ◽  
Markovian Jump ◽  
Replay Attack ◽  
Takagi Sugeno ◽  
Nonlinear Networked Control System

This article investigates the stabilization problem of a nonlinear networked control system (NCS) exposed to a replay attack. A new mathematical model of the replay attack is proposed. The resulting closed-loop system is defined as a discrete-time Markovian jump linear system (MJLS). Employing the Lyapunov–Krasovskii functional, a sufficient condition for stochastic stability is given in the form of linear matrix inequalities (LMIs). The control law can be obtained by solving these LMIs. Finally, a simulation of an inverted pendulum (IP) with Matlab is developed to illustrate our controller’s efficiency.

Disturbance Attenuation with Minimization of Ellipsoids Restricting Phase Trajectories in Transition and Steady State

2020 ◽  
Vol 21 (4) ◽  
pp. 195-199
Author(s):  
I. B. Furtat ◽  
P. A. Gushchin ◽  
A. A. Peregudin
Keyword(s):  
Steady State ◽  
Linear Matrix Inequalities ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Control Law ◽  
Matrix Inequalities ◽  
Integral Control ◽  
Linear Dynamical Systems ◽  
Transition Mode ◽  
Phase Trajectories

Abstract A new method for attenuation of external unknown bounded disturbances in linear dynamical systems with known parameters is proposed. In contrast to the well known results, the developed static control law ensures that the phase trajectories of the system are located in an ellipsoid, which is close enough to the ball in which the initial conditions are located, as well as provides the best control accuracy in the steady state. To solve the problem, the method of Lyapunov functions and the technique of linear matrix inequalities are used. The linear matrix inequalities allow one to find optimal controller. In addition to the solvability of linear matrix inequalities, a matrix search scheme is proposed that provides the smallest ellipsoid in transition mode and steady state with a small error. The proposed control scheme extends to control linear systems under conditions of large disturbances, for the attenuation of which the integral control law is used. Comparative examples of the proposed method and the method of invariant ellipsoids are given. It is shown that under certain conditions the phase trajectories of a closed-loop system obtained on the basis of the invariant ellipsoid method are close to the boundaries of the smallest ellipsoid for the transition mode, while the obtained control law guarantees the convergence of phase trajectories to the smallest ellipsoid in the steady state. 

Guaranteed Cost Control Approach for a Class of T-S Fuzzy Descriptor Delay Systems

2012 ◽  
Vol 241-244 ◽  
pp. 1148-1153 ◽  
Author(s):  
Wei Hua Tian ◽  
Li Xia Li ◽  
Wei Deng ◽  
Yan Zhao
Keyword(s):  
Controller Design ◽  
Sufficient Conditions ◽  
Descriptor Systems ◽  
Delay Systems ◽  
Linear Matrix ◽  
Control Approach ◽  
Time Varying Delay ◽  
Guaranteed Cost ◽  
Takagi Sugeno ◽  
Varying Delay

A new guaranteed cost controller design approach for a class of Takagi-Sugeno (T-S) fuzzy descriptor systems with time-varying delay is presented. Based on the fuzzy rules and weights, the less conservative sufficient conditions for the existence of guaranteed cost controllers via state feedback are given in terms of linear matrix inequalities (LMIs). This method includes the interactions of the different subsystems into one matrix. And the design of optimal guaranteed cost controller can be formulated to a convex optimization problem. At last, a numerical example is given to illustrate the effectiveness of the proposed method and the perfect performance of the optimal guaranteed cost controller.

The Asymptotical Stability Analysis for Switched Descriptor Systems

2010 ◽  
Vol 29-32 ◽  
pp. 2150-2156 ◽  
Author(s):  
Wei Liu ◽  
Zi Yun Lu
Keyword(s):  
Numerical Simulation ◽  
Stability Analysis ◽  
Time Delay ◽  
Lyapunov Stability Theory ◽  
Asymptotical Stability ◽  
Descriptor Systems ◽  
Linear Matrix ◽  
Control Law ◽  
Matrix Inequality ◽  
Vector Matrix

This paper is concerned with the asymptotical stability analysis for a class of switched uncertain descriptor systems with time-delay. The robustly asymptotical stability of this system is proven by making use of the generalized Lyapunov Stability theory, linear matrix inequality (LMI) tools and multiple Lyapunov function techniques. The conservation of result is greatly reduced by means of introducing the optimal weight matrix and avoiding vector matrix inequality in deducing procedure, in which there is no need of transformation and hypothesis for descriptor systems. The designed control law could surely make switched Descriptor Systems quickly approach the balanceable point. Experimentally, one numerical simulation verifies the effectiveness of this method.

Hinf Control of Uncertain Takagi-Sugeno Fuzzy Descriptor Systems

2013 ◽  
Vol 694-697 ◽  
pp. 2110-2115
Author(s):  
Bao Ping Ma ◽  
Ming Chen
Keyword(s):  
State Feedback ◽  
Descriptor Systems ◽  
Descriptor System ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Control Laws ◽  
Invariant Norm ◽  
Norm Bound ◽  
Takagi Sugeno ◽  
Time Invariant

This paper focuses on the problem of Hinf control for uncertain Takagi-Sugeno fuzzy descriptor system with time-invariant norm-bound uncertainty. Sufficient condition for robust Hinf control with state feedback is derived. It is shown that the control laws can be obtained by solving a set of linear matrix inequalities (LMIs) which is numerically tractable with commercially available software. Numerical example is given to demonstrate the advantage of the proposed method.

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