scholarly journals Simultaneous Fault Detection and Control for Discrete-Time Systems via a Switched Scheme

2015 ◽  
Vol 2015 ◽  
pp. 1-13
Author(s):  
Jian Li ◽  
Xingze Dai
Keyword(s):  
Fault Detection ◽  
Design Method ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Switching Strategy ◽  
Discrete Time Systems ◽  
Step Procedure ◽  
Control Objective ◽  
And Control ◽  
Time Systems

This paper is concerned with the problem of simultaneous fault detection and control for linear systems with a switched scheme. The switched detector/controller is designed simultaneously and generates two signals such that it provides fault tolerance, especially including “destabilizing failure” meanwhile, it generates the residual signal to alarm the fault. When the faults are detected, the detector/controller is switched to reduce the effect of the faults. When the faults are removed, the detector/controller is switched to the original detector/controller to guarantee the control objective. In addition, it has time delay in detection of the faults; then the time-driven switching strategy for asynchronous case is included. Thus a mixed switching strategy is proposed. A two-step procedure is adopted to obtain the solutions through satisfying a set of linear matrix inequalities. Finally, an example is provided to demonstrate the effectiveness of the proposed design method.

Simultaneous Fault Detection and Control for Continuous-Time Switched T-S Fuzzy Systems with State Jumps

2021 ◽  
Author(s):  
Ayyoub Ait Ladel ◽  
Abdellah Benzaouia ◽  
Rachid Outbib ◽  
Mustapha Ouladsine
Keyword(s):  
Fault Detection ◽  
Fuzzy Systems ◽  
Degrees Of Freedom ◽  
Average Dwell Time ◽  
Single Step ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Robust Detection ◽  
And Control ◽  
Detector Design

Abstract This paper addresses the simultaneous fault detection and control (SFDC) issue for switched T-S fuzzy systems with state jumps. The main objective is to design robust detection filters and observer-based controllers to stabilize this system class and, at the same time, detect the presence of faults. Less conservative stability conditions are developed, applying the mode-dependent average dwell time (MDADT) concept, the robust H_{\infty} approach, and the piecewise Lyapunov function (PLF) technique. Based on these conditions, the integrated controller and detector design is formalized in the form of linear matrix inequalities (LMI) instead of bilinear matrix inequalities (BMI). The proposed LMIs determine the controller/ detector gains simultaneously in a single step, thus offering more degrees of freedom in the design. Finally, a numerical example and two real systems examples are studied to prove the applicability and effectiveness of the obtained results.

scholarly journals Computation of the Analytic Center of the Solution Set of the Linear Matrix Inequality Arising in Continuous- and Discrete-Time Passivity Analysis

2020 ◽  
Vol 48 (4) ◽  
pp. 633-659
Author(s):  
Daniel Bankmann ◽  
Volker Mehrmann ◽  
Yurii Nesterov ◽  
Paul Van Dooren
Keyword(s):  
Discrete Time ◽  
Transfer Functions ◽  
Convex Set ◽  
Solution Set ◽  
Linear Matrix ◽  
Analytic Center ◽  
Matrix Equations ◽  
Matrix Inequalities ◽  
Discrete Time Systems ◽  
Time Systems

AbstractIn this paper formulas are derived for the analytic center of the solution set of linear matrix inequalities (LMIs) defining passive transfer functions. The algebraic Riccati equations that are usually associated with such systems are related to boundary points of the convex set defined by the solution set of the LMI. It is shown that the analytic center is described by closely related matrix equations, and their properties are analyzed for continuous- and discrete-time systems. Numerical methods are derived to solve these equations via steepest descent and Newton methods. It is also shown that the analytic center has nice robustness properties when it is used to represent passive systems. The results are illustrated by numerical examples.

EXPERIMENTAL RESULTS ON CHUA'S CIRCUIT ROBUST SYNCHRONIZATION VIA LMIs

2007 ◽  
Vol 17 (09) ◽  
pp. 3199-3209 ◽  
Author(s):  
C. D. CAMPOS ◽  
R. M. PALHARES ◽  
E. M. A. M. MENDES ◽  
L. A. B. TORRES ◽  
L. A. MOZELLI
Keyword(s):  
Discrete Time ◽  
Chaotic Systems ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Chua’S Oscillator ◽  
Laboratory Setup ◽  
Robust Synchronization ◽  
Discrete Time Systems ◽  
Main Ideas ◽  
Time Systems

This paper investigates the synchronization of coupled chaotic systems using techniques from the theory of robust [Formula: see text] control based on Linear Matrix Inequalities. To deal with the synchronization of a class of Lur'e discrete time systems, a project methodology is proposed. A laboratory setup based on Chua's oscillator circuit is used to demonstrate the main ideas of the paper in the context of the problem of information transmission.

scholarly journals Design of a Preview Controller for Discrete-Time Systems Based on LMI

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Li Li ◽  
Fucheng Liao
Keyword(s):  
Steady State ◽  
Discrete Time ◽  
Controller Design ◽  
Design Method ◽  
Reference Signal ◽  
Original System ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Discrete Time Systems ◽  
Time Systems

A preview controller design method for discrete-time systems based on LMI is proposed. First, we use the difference between a system state and its steady-state value, instead of the usual difference between system states, to transform the tracking problem into a regulator problem. Then, based on the Lyapunov stability theory and linear matrix inequality (LMI) approach, the preview controller ensuring asymptotic stability of the closed-loop system for the derived augmented error system is found. And an extended functional observer is designed in this paper which can achieve disturbance attenuation in the estimation process; as a result, the state of the system can be reconstructed rapidly and accurately. The controller gain matrix is obtained by solving an LMI problem. By incorporating the controller obtained into the original system, we obtain the preview controller of the system under consideration. To make sure that the output tracks the reference signal without steady-state error, an integrator is introduced. The numerical simulation example also illustrates the effectiveness of the results in the paper.

Robust Control Design for Retarded Discrete-Time Systems

2006 ◽  
Vol 129 (1) ◽  
pp. 72-76 ◽  
Author(s):  
El Houssaine Tissir
Keyword(s):  
Linear Matrix Inequalities ◽  
Discrete Time ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Synthesis Methods ◽  
Matrix Inequalities ◽  
Stabilizing Controller ◽  
Discrete Time Systems ◽  
Robust Control Design ◽  
Time Systems

This paper focuses on the analysis and synthesis of a robust stabilizing controller for linear discrete time systems with norm-bounded time varying uncertainties. Delay independent robust stability conditions are derived and two synthesis methods are presented. One method is to construct a robust memoryless state feedback control law from the solutions of linear matrix inequalities. The other method consists of designing robust observer-based output feedback controller. The results are expressed in termes of linear matrix inequalities. A comparison with μ∕LDI tests is presented. Furthermore, numerical examples are given for illustration.

Non-Fragile Robust H∞ Control for Linear Uncertain Switched Systems with Delayed Perturbations

2012 ◽  
Vol 562-564 ◽  
pp. 1968-1971
Author(s):  
Ze Yin Xu
Keyword(s):  
Switched Systems ◽  
State Feedback ◽  
Design Method ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Switching Strategy ◽  
Controller Gain ◽  
Simulation Results ◽  
Environment Parameters ◽  
The Given

The non-fragile robust H∞ controller was designed for a class of uncertain switched systems with delayed perturbations under additive perturbations of controller gain. A sufficient condition for the solvability of the non-fragile robust H∞ controller via state feedback was proved and presented, which based on a proper Lyapunov function and switching strategy, non-fragile robust H∞ controller can be obtained only by solving linear matrix inequalities. The systems under actions of the given controller are not only robust but also satisfy H∞ performance when controller changes, and thus have better adaptability against variety of the environment parameters. The simulation results show the effectiveness of the design method.

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